文章基本信息

标题：Connection probabilities in Poisson random graphs with uniformly bounded edges
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作者：Alessandra Faggionato ; Hlafo Alfie Mimun
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：463-486
DOI：10.30757/ALEA.v16-18
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider random graphs with uniformly bounded edges on a Poissonpoint process conditioned to contain the origin. In particular we focus on therandom connection model, the Boolean model and the Miller{Abrahams randomresistor network with lower{bounded conductances. The latter is relevant for theanalysis of conductivity by Mott variable range hopping in strongly disorderedsystems. By using the method of randomized algorithms developed by Duminil{Copin et al. we prove that in the subcritical phase the probability that the originis connected to some point at distance n decays exponentially in n, while in thesupercritical phase the probability that the origin is connected to innity is strictlypositive and bounded from below by a term proportional to ( 􀀀 c), being thedensity of the Poisson point process and c being the critical density.
关键词：Poisson Point Process; Random Connection Model; Boolean Model;Mott Variable Range Hopping; Miller{Abrahams Resistor Network; Connection Probability; Ran;;domized Algorithm;