Semantic Scholar Open Access 2024 2 sitasi

All Spatial Random Graphs with Weak Long-Range Effects have Chemical Distance Comparable to Euclidean Distance

Lukas Lüchtrath

Abstrak

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).

Topik & Kata Kunci

Mathematics

Penulis (1)

Lukas Lüchtrath

Format Sitasi

APA MLA BibTeX

Lüchtrath, L. (2024). All Spatial Random Graphs with Weak Long-Range Effects have Chemical Distance Comparable to Euclidean Distance. https://doi.org/10.1007/s10959-025-01467-0

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Total Sitasi: 2×
Sumber Database: Semantic Scholar
DOI: 10.1007/s10959-025-01467-0
Akses: Open Access ✓