2006/07/31 by Jean-Baptiste Gouéré · 9 citations
Mathematics · Medicine · Physics and Astronomy · #Growth model #Mathematical and Theoretical Epidemiology and Ecology Models #Percolation (cognitive psychology) #Process (computing) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Type (biology) #Vertex (graph theory) #math.PR #msc:60K35
paper · pdf · doi:10.1214/105051607000000113
published in The Annals of Applied Probability 17(4) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/105051607000000113 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/08/01 · arxiv created 2007/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study two competing growth models. Each of these models describes the spread of a finite number of infections on a graph. Each infection evolves like an (oriented or unoriented) first passage percolation process except that once a vertex is infected by type i infection, it remains of type i forever. We give results about the shape of the area ultimately infected by the different infections.