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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 language  English 

Pages (fromto)  35473569 
Number of pages  23 
Journal  Stochastic Processes and their Applications 
Volume  129 
Issue number  9 
Early online date  5 Oct 2018 
DOIs  
Publication status  Published  1 Sept 2019 
Bibliographical note
The text has been improved throughout and the proofs clarifiedKeywords
 math.PR
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Dive into the research topics of 'Random walks in random conductances: decoupling and spread of infection'. Together they form a unique fingerprint.Projects
 1 Finished

Early Career Fellowship  Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A.
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council