Expansion of the critical intensity for the random connection model

Abstract We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk model, the hyper-cubic model, the Gaussian connection kernel, and a coordinate-wise Cauchy kernel.

Authors

Markus Heydenreich (ORCID: https://orcid.org/0000-0002-3749-7431)
Matthew Dickson (ORCID: https://orcid.org/0000-0002-8629-4796)

Institutions

University of British Columbia (CA)
University of Augsburg (DE)

Publication Details

Journal: Combinatorics Probability Computing
Published: 2024-11-08
DOI: https://doi.org/10.1017/s0963548324000270
Primary Topic: Stochastic processes and statistical mechanics
Type: article
Field-Weighted Citation Impact: 0.00

Funders

Deutsche Forschungsgemeinschaft

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article

Expansion of the critical intensity for the random connection model

Markus Heydenreich, Matthew Dickson

Nov 8, 2024

Combinatorics Probability Computing

Stochastic processes and statistical mechanics

article

Expansion of the critical intensity for the random connection model

Markus Heydenreich, Matthew Dickson

November 8, 2024article en

Abstract

Abstract We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk model, the hyper-cubic model, the Gaussian connection kernel, and a coordinate-wise Cauchy kernel.

Combinatorics Probability ComputingVol. 34(2)

University of British Columbia (CA), University of Augsburg (DE)

Deutsche Forschungsgemeinschaft

Openalex Percentile: Top 67%

Stochastic processes and statistical mechanics

DOI Open Access PDF OpenAlex

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