| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Weizmann Inst Sci, Dept Math, Rehovot - Israel
[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[3] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge - England
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | ANNALS OF APPLIED PROBABILITY; v. 30, n. 1, p. 208-258, FEB 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson(lambda) particles per site, with one additional active particle planted at some vertex o of a finite connected simple graph G = (V, E). Initially, only the particles occupying o are active. Active particles perform t is an element of N boolean OR [infinity] steps of the walk they picked before vanishing and activate all inactive particles they hit. This system is often taken as a model for the spread of an epidemic over a population. Let R-t be the set of vertices which are visited by the process, when active particles vanish after t steps. We study the susceptibility of the process on the underlying graph, defined as the random quantity S(G) := inf[t : R-t = V] (essentially, the shortest particles' lifespan required for the entire population to get infected). We consider the cases that the underlying graph is either a regular expander or a d-dimensional torus of side length n (for all d >= 1) T-d(n) and determine the asymptotic behavior of S up to a constant factor. In fact, throughout we allow the particle density lambda to depend on n and for d >= 2 we determine the asymptotic behavior of S(T-d(n)) up to smaller order terms for a wide range of lambda = lambda(n). (AU) | |
| FAPESP's process: | 17/10555-0 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |