{"results":[{"id":"ss_45f56c3f513d661f3c3bbad434c0dda46c339de3","title":"Indistinguishability of cells for the ideal Poisson Voronoi tessellation","authors":[{"name":"Sam Mellick"}],"abstract":"In this note, we resolve a question of D’Achille, Curien, Enriquez, Lyons, and Ünel [ arXiv:2303.16831 [math.PR] , 2023] by showing that the cells of the ideal Poisson Voronoi tessellation are indistinguishable. This follows from an application of the Howe-Moore theorem and a theorem of Meyerovitch about the nonexistence of thinnings of the Poisson point process. We also give an alternative proof of Meyerovitch’s theorem.","source":"Semantic Scholar","year":2026,"language":"en","subjects":null,"doi":"10.1090/proc/17493","url":"https://www.semanticscholar.org/paper/45f56c3f513d661f3c3bbad434c0dda46c339de3","is_open_access":true,"published_at":"","score":70},{"id":"ss_352812bb85c6c76f94019912d4ac3aa426baa543","title":"Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise","authors":[{"name":"Kazuo Yamazaki"}],"abstract":"We consider the one-dimensional Burgers' equation forced by fractional derivative of order $\\frac{1}{2}$ applied on space-time white noise. Relying on the approaches of Anderson Hamiltonian from Allez and Chouk (2015, arXiv:1511.02718 [math.PR]) and two-dimensional Navier-Stokes equations forced by space-time white noise from Hairer and Rosati (2024, Annals of PDE, \\textbf{10}, pp. 1--46), we prove the global-in-time existence and uniqueness of its mild and weak solutions.","source":"Semantic Scholar","year":2025,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/352812bb85c6c76f94019912d4ac3aa426baa543","is_open_access":true,"citations":1,"published_at":"","score":69.03},{"id":"arxiv_2512.08166","title":"Conditions for Equivalence of Random Interlacements and Random Walk Reflected off of Infinity","authors":[{"name":"Yao Yu"}],"abstract":"On a transient weighted graph, there are two models of random walk which continue after reaching infinity: random interlacements, and random walk reflected off of infinity, recently introduced in arXiv:2506.18827 [math.PR]. We prove these two models are equivalent if and only if all harmonic functions of the underlying graph with finite Dirichlet energy are constant functions, or equivalently, the free and wired spanning forests coincide. In particular, examples where the models are equivalent include $\\mathbb{Z}^d$, cartesian products, and many Cayley graphs, while examples that fail the condition include all transient trees.","source":"arXiv","year":2025,"language":"en","subjects":["math.PR"],"url":"https://arxiv.org/abs/2512.08166","pdf_url":"https://arxiv.org/pdf/2512.08166","is_open_access":true,"published_at":"2025-12-09T01:50:34Z","score":69},{"id":"doaj_10.24072/pcjournal.614","title":"Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics\n","authors":[{"name":"Hoessly, Linard"},{"name":"Wiuf, Carsten"},{"name":"Xia, Panqiu"}],"abstract":"Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks (SRNs),modelled as continuous time Markov chains (CTMCs) and their stationary distributions. We are interested in complex-balanced stationary distributions, where the probability flow out of a  complex equals the flow into the complex.  We   characterise the existence and the form of complex-balanced distributions of SRNs with arbitrary transition functions through conditions on the cycles of the reaction graph (a digraph). Furthermore, we   give a sufficient condition for the existence of a complex-balanced distribution  and give precise conditions for when it is also necessary. The sufficient condition is also necessary for mass-action kinetics (and certain generalisations of that) or if the connected components of the digraph are cycles.  Moreover,  we state a deficiency theorem, a generalisation of the deficiency theorem for stochastic mass-action kinetics to arbitrary stochastic kinetics. The theorem gives the co-dimension of the parameter space for which a complex-balanced distribution exists. To achieve this, we construct an iterative procedure to decompose a strongly connected reaction graph into disjoint cycles, such that the corresponding SRN has equivalent dynamics and preserves complex-balancedness, provided the original SRN had so. This decomposition might have independent interest and might be applicable to  edge-labelled digraphs in general. ","source":"DOAJ","year":2025,"language":"","subjects":["Archaeology","Science"],"doi":"10.24072/pcjournal.614","url":"https://peercommunityjournal.org/articles/10.24072/pcjournal.614/","is_open_access":true,"published_at":"","score":69},{"id":"ss_b1c5ad88be1cf3010e54704c38f5dacbe4fc3f39","title":"Uniform log-Sobolev inequalities for mean field particles with flat-convex energy","authors":[{"name":"Song-bo Wang"}],"abstract":"The purpose of this short note is to demonstrate uniform logarithmic Sobolev inequalities for the mean field gradient particle systems associated to an energy functional that is convex in the flat sense. A defective log-Sobolev inequality was already established implicitly in a previous joint work with F. Chen and Z. Ren [arXiv:2212.03050 [math.PR]]. It remains only to tighten it by a uniform Poincar\\'e inequality, which we prove by the method in a recent work of Guillin, W. Liu, L. Wu and C. Zhang [Ann. Appl. Probab., 32(3):1590-1614, 2022]. As an application, we show that the particle system exhibits the concentration of measure phenomenon in the long time.","source":"Semantic Scholar","year":2024,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/b1c5ad88be1cf3010e54704c38f5dacbe4fc3f39","is_open_access":true,"citations":13,"published_at":"","score":68.39},{"id":"ss_c9ff29664f2def459a543cdfc0ce95eda5c623c8","title":"All Spatial Random Graphs with Weak Long-Range Effects have Chemical Distance Comparable to Euclidean Distance","authors":[{"name":"Lukas Lüchtrath"}],"abstract":"This note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is based on the scarceness of long edges in the graph and weak correlations at large distances and is valid for all translation invariant and locally finite graphs that fulfil these conditions. We apply the result to various examples, thereby confirming a conjecture on graph distances in the heavy-tailed Boolean model posed by Hirsch (Braz J Probab Stat 31(1):111–143, 2017). The proof is based on a renormalisation scheme introduced by Berger (arXiv:math/0409021 [math.PR], 2004).","source":"Semantic Scholar","year":2024,"language":"en","subjects":["Mathematics"],"doi":"10.1007/s10959-025-01467-0","url":"https://www.semanticscholar.org/paper/c9ff29664f2def459a543cdfc0ce95eda5c623c8","is_open_access":true,"citations":2,"published_at":"","score":68.06},{"id":"ss_26e2a0cd91ff0b6d3e9f6bc31b72200368cb8997","title":"Analysis of the chemical diffusion master equation for creation and mutual annihilation reactions","authors":[{"name":"Alberto Lanconelli"},{"name":"Berk Tan Perçin"}],"abstract":"We propose an infinite dimensional generating function method for finding the analytical solution of the so-called chemical diffusion master equation (CDME) for creation and mutual annihilation chemical reactions. CDMEs model by means of an infinite system of coupled Fokker–Planck equations the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles; here, we focus an creation and mutual annihilation chemical reactions combined with Brownian diffusion of the single particles. Using our method we are able to link certain finite dimensional projections of the solution of the CDME to the solution of a single linear fourth order partial differential equation containing as many variables as the dimension of the aforementioned projection space. Our technique extends the one presented in Lanconelli [J. Math. Anal. Appl. 526, 127352 (2023)] and Lanconelli et al. [arXiv:2302.10700 [math.PR] (2023)] which allowed for an explicit representation for the solution of birth-death type CDMEs.","source":"Semantic Scholar","year":2024,"language":"en","subjects":null,"doi":"10.1063/5.0163100","url":"https://www.semanticscholar.org/paper/26e2a0cd91ff0b6d3e9f6bc31b72200368cb8997","pdf_url":"https://cris.unibo.it/bitstream/11585/966236/1/Mutual_annihilation_revision.pdf","is_open_access":true,"citations":1,"published_at":"","score":68.03},{"id":"ss_0d812c5a94c6997c5f41e76f805bfdd5b6df4859","title":"Moments of partition functions of 2D Gaussian polymers in the weak disorder regime – II","authors":[{"name":"Clément Cosco"},{"name":"O. Zeitouni"}],"abstract":"Let $W_N(\\beta) = \\mathrm{E}_0\\left[e^{ \\sum_{n=1}^N \\beta \\omega(n,S_n) - N\\beta^2/2}\\right]$ be the partition function of a two-dimensional directed polymer in a random environment, where $\\omega(i,x), i\\in \\mathbb{N}, x\\in \\mathbb{Z}^2$ are i.i.d. standard normal and $\\{S_n\\}$ is the path of a random walk. With $\\beta=\\beta_N=\\widehat{\\beta} \\sqrt{\\pi/\\log N}$ and $\\widehat{\\beta}\\in (0,1)$ (the subcritical window), $\\log W_N(\\beta_N)$ is known to converge in distribution to a Gaussian law of mean $-\\lambda^2/2$ and variance $\\lambda^2$, with $\\lambda^2=\\log ((1-\\widehat\\beta^2)^{-1})$ (Caravenna, Sun, Zygouras, Ann. Appl. Probab. (2017)). We study in this paper the moments $\\mathbb E [W_N( \\beta_N)^q]$ in the subcritical window, and prove a lower bound that matches for $q=O(\\sqrt{\\log N})$ the upper bound derived by us in Cosco, Zeitouni, arXiv:2112.03767 [math.PR]. The analysis is based on appropriate decouplings and a Poisson convergence that uses the method of ''two moments suffice''.","source":"Semantic Scholar","year":2023,"language":"en","subjects":["Mathematics"],"doi":"10.1214/24-ejp1148","url":"https://www.semanticscholar.org/paper/0d812c5a94c6997c5f41e76f805bfdd5b6df4859","pdf_url":"https://doi.org/10.1214/24-ejp1148","is_open_access":true,"citations":14,"published_at":"","score":67.42},{"id":"ss_36e09ddc07c649cb47e9017a3d39d7500968f95a","title":"Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise","authors":[{"name":"K. Yamazaki"}],"abstract":"We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2002, J. Funct. Anal., \\textbf{196}, pp. 180--210) on the Navier-Stokes equations does not seem to fit. We follow instead the approach of Hairer and Rosati (2023, arXiv:2301.11059 [math.PR]), take advantage of the structure of Maxwell's equation, such as anti-symmetry, to find an appropriate paracontrolled ansatz and many crucial cancellations, and prove the global-in-time existence and uniqueness of its solution.","source":"Semantic Scholar","year":2023,"language":"en","subjects":["Mathematics"],"doi":"10.1016/j.spa.2026.104893","url":"https://www.semanticscholar.org/paper/36e09ddc07c649cb47e9017a3d39d7500968f95a","is_open_access":true,"citations":4,"published_at":"","score":67.12},{"id":"crossref_10.1007/s11856-023-2563-z","title":"ℤ/pr-hyperbolicity via homology","authors":[{"name":"Guy Boyde"}],"abstract":"AbstractWe show that the homotopy groups of a Moore space Pn(pr), where pr ≠ 2, are ℤ/ps-hyperbolic for s ≤ r. Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ps-hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/pr-hyperbolic, and deduce some examples.","source":"CrossRef","year":2023,"language":"en","subjects":null,"doi":"10.1007/s11856-023-2563-z","url":"https://doi.org/10.1007/s11856-023-2563-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11856-023-2563-z.pdf","is_open_access":true,"citations":4,"published_at":"","score":67.12},{"id":"doaj_10.46298/jtcam.8322","title":"A probabilistic model for fast-to-evaluate 2D crack path prediction in heterogeneous materials","authors":[{"name":"Kathleen Pele"},{"name":"Jean Baccou"},{"name":"Loïc Daridon"},{"name":"Jacques Liandrat"},{"name":"Thibaut Le Gouic"},{"name":"Yann Monerie"},{"name":"Frédéric Péralès"}],"abstract":"This paper is devoted to the construction of a new fast-to-evaluate model for the prediction of 2D crack paths in concrete-like microstructures. The model generates piecewise linear cracks paths with segmentation points selected using a Markov chain model. The Markov chain kernel involves local indicators of mechanical interest and its parameters are learnt from numerical full-field 2D simulations of cracking using a cohesive-volumetric finite element solver called XPER. This model does not include any mechanical elements. It is the database, derived from the XPER crack, that contains the mechanical information and optimizes the probabilistic model. The resulting model exhibits a drastic improvement of CPU time in comparison to simulations from XPER.","source":"DOAJ","year":2023,"language":"","subjects":["Mechanics of engineering. Applied mechanics"],"doi":"10.46298/jtcam.8322","url":"https://jtcam.episciences.org/8322/pdf","pdf_url":"https://jtcam.episciences.org/8322/pdf","is_open_access":true,"published_at":"","score":67},{"id":"ss_267d99b4d76337300cb3fae0c1d3a0250928318c","title":"Non-uniqueness in law for the Boussinesq system forced by random noise","authors":[{"name":"K. Yamazaki"}],"abstract":"Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by random noise was established recently in Hofmanová et al. (2019, arXiv:1912.11841 [math.PR]). The purpose of this work is to prove non-uniqueness in law for the Boussinesq system forced by random noise. Diffusion within the equation of its temperature scalar field has a full Laplacian and the temperature scalar field can be initially smooth.","source":"Semantic Scholar","year":2021,"language":"en","subjects":["Mathematics"],"doi":"10.1007/s00526-022-02285-6","url":"https://www.semanticscholar.org/paper/267d99b4d76337300cb3fae0c1d3a0250928318c","pdf_url":"https://arxiv.org/pdf/2101.05411","is_open_access":true,"citations":17,"published_at":"","score":65.50999999999999},{"id":"ss_3e2069f2496bf0d72ec402b6d74ebe2eb3f6f62c","title":"Ramification of Volterra-type rough paths","authors":[{"name":"Y. Bruned"},{"name":"Foivos Katsetsiadis"}],"abstract":"We extend the new approach introduced in arXiv:1912.02064v2 [math.PR] and arXiv:2102.10119v1 [math.PR] for dealing with stochastic Volterra equations using the ideas of Rough Path theory and prove global existence and uniqueness results. The main idea of this approach is simple: Instead of the iterated integrals of a path comprising the data necessary to solve any equation driven by that path, now iterated integral convolutions with the Volterra kernel comprise said data. This leads to the corresponding abstract objects called Volterra-type Rough Paths, as well as the notion of the convolution product, an extension of the natural tensor product used in Rough Path Theory.","source":"Semantic Scholar","year":2021,"language":"en","subjects":["Mathematics"],"doi":"10.1214/22-ejp890","url":"https://www.semanticscholar.org/paper/3e2069f2496bf0d72ec402b6d74ebe2eb3f6f62c","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Ramification-of-Volterra-type-rough-paths/10.1214/22-EJP890.pdf","is_open_access":true,"citations":4,"published_at":"","score":65.12},{"id":"arxiv_2105.03423","title":"Ramification of Volterra-type Rough Paths","authors":[{"name":"Yvain Bruned"},{"name":"Foivos Katsetsiadis"}],"abstract":"We extend the new approach introduced in arXiv:1912.02064v2 [math.PR] and arXiv:2102.10119v1 [math.PR] for dealing with stochastic Volterra equations using the ideas of Rough Path theory and prove global existence and uniqueness results. The main idea of this approach is simple: Instead of the iterated integrals of a path comprising the data necessary to solve any equation driven by that path, now iterated integral convolutions with the Volterra kernel comprise said data. This leads to the corresponding abstract objects called Volterra-type Rough Paths, as well as the notion of the convolution product, an extension of the natural tensor product used in Rough Path Theory.","source":"arXiv","year":2021,"language":"en","subjects":["math.PR","math.AP","math.RA"],"url":"https://arxiv.org/abs/2105.03423","pdf_url":"https://arxiv.org/pdf/2105.03423","is_open_access":true,"published_at":"2021-05-07T17:54:42Z","score":65},{"id":"ss_663f7e1f93d3f5b6932d36de7b6d4aa99848e1a4","title":"Remarks on the non-uniqueness in law of the Navier–Stokes equations up to the J.-L. Lions’ exponent","authors":[{"name":"K. Yamazaki"}],"abstract":"Lions (1959, Bull. Soc. Math. France, \\textbf{87}, 245--273) introduced the Navier-Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanov$\\acute{\\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]), we prove the non-uniqueness in law for the three-dimensional stochastic Navier-Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.","source":"Semantic Scholar","year":2020,"language":"en","subjects":["Mathematics"],"doi":"10.1016/j.spa.2022.01.016","url":"https://www.semanticscholar.org/paper/663f7e1f93d3f5b6932d36de7b6d4aa99848e1a4","pdf_url":"https://arxiv.org/pdf/2006.11861","is_open_access":true,"citations":26,"published_at":"","score":64.78},{"id":"ss_3d7f1872f139dc26ac6613fe93e077e03d41565b","title":"NonUniqueness in Law for Two-Dimensional Navier-Stokes Equations with Diffusion Weaker than a Full Laplacian","authors":[{"name":"K. Yamazaki"}],"abstract":"We study the two-dimensional Navier-Stokes equations forced by random noise with a diffusive term generalized via a fractional Laplacian that has a positive exponent strictly less than one. Because intermittent jets are inherently three-dimensional, we instead adapt the theory of intermittent form of the two-dimensional stationary flows to the stochastic approach presented by Hofmanov$\\acute{\\mathrm{a}}$, Zhu $\\\u0026$ Zhu (2019, arXiv:1912.11841 [math.PR]) and prove its non-uniqueness in law.","source":"Semantic Scholar","year":2020,"language":"en","subjects":["Computer Science","Mathematics"],"doi":"10.1137/21m1451087","url":"https://www.semanticscholar.org/paper/3d7f1872f139dc26ac6613fe93e077e03d41565b","pdf_url":"https://arxiv.org/pdf/2008.04760","is_open_access":true,"citations":21,"published_at":"","score":64.63},{"id":"ss_631693d4c85e0f2ce04f817bad8a82312f8fb51e","title":"KPZ equation from non-simple variations on open ASEP","authors":[{"name":"Kevin Yang"}],"abstract":"This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP from Corwin and Shen (Commun Pure Appl Math 71(10):2065–2128, 2018), Parekh (Commun Math Phys 365:569–649, 2019. https://doi.org/10.1007/s00220-018-3258-x). but admitting non-simple interactions both at the boundary and within the bulk of the particle system. These variations on open-ASEP are not integrable models, similar to the long-variations on ASEP considered in Dembo and Tsai (Commun Math Phys 341(1):219–261, 2016), Yang (Kardar–Parisi–Zhang equation from long-range exclusion processes, 2020. arXiv:2002.05176 [math.PR]). We establish the KPZ equation with the appropriate Robin boundary conditions as scaling limits for height function fluctuations associated to these non-integrable models, providing further evidence for the aforementioned universality of the KPZ equation. We specialize to compact domains and address non-compact domains in a second paper (Yang in KPZ equation from non-simple dynamics with boundary in the non-compact regime). The procedure that we employ to establish the aforementioned theorem is the second main point of this paper. Invariant measures in the presence of boundary interactions generally lack reasonable descriptions. Thus, global analyses done through the invariant measure, including the theory of energy solutions in Goncalves and Jara (Arch Ration Mech Anal 212:597, 2014), Goncalves and Jara (Stoch Process Appl 127(12):4029–4052, 2017), Goncalves et al. (Ann Probab 43(1):286–338, 2015), is immediately obstructed. To circumvent this obstruction, we appeal to the almost entirely local nature of the analysis in Yang (2020).","source":"Semantic Scholar","year":2020,"language":"en","subjects":["Mathematics","Physics"],"doi":"10.1007/s00440-022-01133-0","url":"https://www.semanticscholar.org/paper/631693d4c85e0f2ce04f817bad8a82312f8fb51e","is_open_access":true,"citations":11,"published_at":"","score":64.33},{"id":"arxiv_2003.14145","title":"New approach to greedy vector quantization","authors":[{"name":"Rancy El Nmeir"},{"name":"Harald Luschgy"},{"name":"Gilles Pagès"}],"abstract":"We extend some rate of convergence results of greedy quantization sequences already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general class of distributions satisfying a certain control, that the quantization error of these sequences have an $n^{-\\frac1d}$ rate of convergence and that the distortion mismatch property is satisfied. We will give some non-asymptotic Pierce type estimates. The recursive character of greedy vector quantization allows some improvements to the algorithm of computation of these sequences and the implementation of a recursive formula to quantization-based numerical integration. Furthermore, we establish further properties of sub-optimality of greedy quantization sequences.","source":"arXiv","year":2020,"language":"en","subjects":["math.PR"],"url":"https://arxiv.org/abs/2003.14145","pdf_url":"https://arxiv.org/pdf/2003.14145","is_open_access":true,"published_at":"2020-03-31T12:30:31Z","score":64}],"total":1146073,"page":1,"page_size":20,"sources":["arXiv","DOAJ","Semantic Scholar","CrossRef"],"query":"math.PR"}