Random walks in random conductances: decoupling and spread of infection

Peter Gracar, Alexandre Stauffer

Research output: Contribution to journalArticle

18 Downloads (Pure)

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

Keywords

  • math.PR

Fingerprint Dive into the research topics of 'Random walks in random conductances: decoupling and spread of infection'. Together they form a unique fingerprint.

  • Projects

    Cite this