A phase transition in a model for the spread of an infection
| dc.creator | Kesten, Harry | |
| dc.creator | Sidoravicius, Vladas | |
| dc.date | 2004-10-17 | |
| dc.date.accessioned | 2026-07-07T05:13:20Z | |
| dc.date.available | 2026-07-07T05:13:20Z | |
| dc.description | We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected, respectively. All particles perform independent, continuous time, simple random walks on Z^d with the same jump rate D. The only interaction between the particles is that at the moment when a B-particle jumps to a site which contains an A-particle, or vice versa, the A-particle turns into a B-particle. All B-particles recuperate (that is, turn back into A-particles) independently of each other at a rate lamda. We assume that we start the system with N_A(x,0-) A-particles at x, and that the N_A(x,0-), x in Z^d, are i.i.d., mean mu_A Poisson random variables. In addition we start with one additional B-particle at the origin. We show that there is a critical recuperation rate lambda_c > 0 such that the B-particles survive (globally) with positive probability if lambda < lamda_c and die out with probability 1 if lambda > \lamda_c. | |
| dc.description | 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0410371 | |
| dc.identifier | http://arxiv.org/abs/math/0410371 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72908 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35 (primary); 60J15 (secondary) | |
| dc.title | A phase transition in a model for the spread of an infection | |
| dc.type | text |