A shape theorem for the spread of an infection
| dc.creator | Kesten, Harry | |
| dc.creator | Sidoravicius, Vladas | |
| dc.date | 2003-12-31 | |
| dc.date.accessioned | 2026-07-07T05:04:17Z | |
| dc.date.available | 2026-07-07T05:04:17Z | |
| dc.description | We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are called A-particles and move independently of each other. We assume that we start the system with a Poisson number of particles at each lattice site x, with the number of particles at different x's i.i.d. In addition, there are a finite number of B-particles which perform the same continuous time simple random walks as the A-particles. A- and B-particles are interpreted as individuals who are healthy or infected, respectively. The B-particles move independently of each other. The only interaction is that when a B-particle and an A-particle coincide, the latter instantaneously turns into a B-particle. Let B(t) be the set of sites visited by a B-particle during [0,t]. We show that B(t) grows linearly in time and has an asymptotic shape; more precisely, there exists a non-random convex, compact set B_0 such that almost surely, for all 0 < a <1, (1-a)tB_0 is contained in B(t) and B(t) is contained in (1+a)tB_0 eventually. | |
| dc.description | 59 pages in AMSTex format plus 1 figure in eps format | |
| dc.identifier | https://arxiv.org/abs/math/0312511 | |
| dc.identifier | http://arxiv.org/abs/math/0312511 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69744 | |
| dc.subject | Probability | |
| dc.subject | 60K35 (Primary), 60J15 (Secondary) | |
| dc.title | A shape theorem for the spread of an infection | |
| dc.type | text |