Random walks in random conductances

decoupling and spread of infection

Peter Gracar, Alexandre Stauffer

Research output: Contribution to journalArticle

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Abstract

Let (G,μ) be a uniformly elliptic random conductance graph on Z d with a Poisson point process of particles at time t=0 that perform independent simple random walks. We show that inside a cube Q K of side length K, if all subcubes of side length ℓ<K inside Q K have sufficiently many particles, the particles return to stationarity after cℓ 2 time with a probability close to 1. We show that in this setup, an infection spreads with positive speed in any direction. Our framework is robust enough to allow us to also extend the result to infection with recovery.

Original languageEnglish
Pages (from-to)3547-3569
Number of pages23
JournalStochastic Processes and their Applications
Volume129
Issue number9
Early online date5 Oct 2018
DOIs
Publication statusPublished - 1 Sep 2019

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Conductance
Decoupling
Infection
Random walk
Recovery
Poisson Point Process
Simple Random Walk
Stationarity
Regular hexahedron
Graph in graph theory

Keywords

  • math.PR

Cite this

Random walks in random conductances : decoupling and spread of infection. / Gracar, Peter; Stauffer, Alexandre.

In: Stochastic Processes and their Applications, Vol. 129, No. 9, 01.09.2019, p. 3547-3569.

Research output: Contribution to journalArticle

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