ﻻ يوجد ملخص باللغة العربية
We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on ${mathbb Z}^d,dge 3$, when there is no extinction of the infection. For this, we derive percolation estimates (using dynamic renormalization techniques) for a locally dependent random graph in correspondence with the epidemic model.
We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On ${mathbb Z}^d$, RWDE are parameterized b
We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $Z^d$, RWDE are parameterized by a $2d$-
We study a particular model of a random medium, called the orthant model, in general dimensions $dge 2$. Each site $xin Z^d$ independently has arrows pointing to its positive neighbours $x+e_i$, $i=1,dots, d$ with probability $p$ and otherwise to its
We consider two approaches to study the spread of infectious diseases within a spatially structured population distributed in social clusters. According whether we consider only the population of infected individuals or both populations of infected i
We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the $d$