Abstract
We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected region when infected and susceptible particles move at the same speed. In this paper we establish a linear growth rate when infected and susceptible particles move at different speeds, answering an open problem from their work. Our proof combines an intricate coupling of Poisson processes with a streamlined version of a percolation model of Sidoravicius and Stauffer.
Original language | English (US) |
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Pages (from-to) | 73-131 |
Number of pages | 59 |
Journal | Probability Theory and Related Fields |
Volume | 187 |
Issue number | 1-2 |
DOIs | |
State | Published - Oct 2023 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Growth model
- Infection spread
- Interacting particle systems
- Random walks