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 |
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Article number | 135 |
Pages (from-to) | 1-28 |
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.
Funding
*Supported by EPSRC Fellowship EP/N004566/1. †Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands. E-mail: [email protected] ‡Università Roma Tre, Dip. di Matematica e Fisica, Largo S. Murialdo 1, 00146, Rome, Italy; University of Bath, Dept of Mathematical Sciences, BA2 7AY Bath, UK. E-mail: [email protected]
Keywords
- biased random walks
- infection processes
- interacting particle systems
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Dive into the research topics of 'Local survival of spread of infection among biased random walks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Early Career Fellowship - Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A. (PI)
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council