Projects per year
Abstract
We study infection spread among biased random walks on Z ^{d} . The random walks move independently and an infected particle is placed at the origin at time zero. Infection spreads instantaneously when particles share the same site and there is no recovery. If the initial density of particles is small enough, the infected cloud travels in the direction of the bias of the random walks, implying that the infection does not survive locally. When the density is large, the infection spreads to the whole Z ^{d} . The proofs rely on two different techniques. For the small density case, we use a description of the infected cloud through genealogical paths, while the large density case relies on a renormalization scheme.
Original language  English 

Article number  135 
Pages (fromto)  128 
Journal  Electronic Journal of Probability 
Volume  27 
Early online date  6 Oct 2022 
DOIs  
Publication status  Published  31 Dec 2022 
Bibliographical note
Funding Information:*Supported by EPSRC Fellowship EP/N004566/1.
Keywords
 biased random walks
 infection processes
 interacting particle systems
ASJC Scopus subject areas
 Statistics and Probability
 Statistics, Probability and Uncertainty
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 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