Semantic Scholar Open Access 2021 2 sitasi

Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes

Tobias Johnson E. Peköz

Lihat Sumber DOI

Abstrak

Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed point equations to obtain uniform error bounds for generalized gamma approximations using Stein's method. Here we show how monotone couplings arising with these fixed point equations can be used to obtain sharper tail bounds that, in many cases, outperform competing moment-based bounds and the uniform bounds obtainable with Stein's method. Applications are given to concentration inequalities for preferential attachment random graphs, branching processes, random walk local time statistics and the size of random subtrees of uniformly random binary rooted plane trees.

Topik & Kata Kunci

Mathematics

Penulis (2)

Tobias Johnson

E. Peköz

Format Sitasi

APA MLA BibTeX

Johnson, T., Peköz, E. (2021). Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes. https://doi.org/10.1016/j.spa.2022.06.012

Akses Cepat

Lihat di Sumber doi.org/10.1016/j.spa.2022.06.012

Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Total Sitasi: 2×
Sumber Database: Semantic Scholar
DOI: 10.1016/j.spa.2022.06.012
Akses: Open Access ✓