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19972026
most citedNetworks beyond pairwise interactions: structure and dynamics

1.6k citations

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Showing 2011 · math.PRShow all

9 papers · 2 filters

math.PR2011★ 3 cited

A shape theorem for an epidemic model in dimension

Enrique Andjel, Nicolas Chabot, Ellen Saada

We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on , when there is no…

math.PR2011

Regular -measures are not always Gibbsian

Roberto Fernández, Sandro Gallo, Grégory Maillard

Regular -measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields dete…

math.PR2011★ 16 cited

Branching Random Walks on Free Products of Groups

Elisabetta Candellero, Lorenz A. Gilch, Sebastian Müller

We study certain phase transitions of branching random walks (BRW) on Cayley graphs of free products. The aim of this paper is to compare the size and structural properties of the…

math.PR2011★ 1 cited

Limit theorems for one and two-dimensional random walks in random scenery

Fabienne Castell, Nadine Guillotin--Plantard, Françoise Pène

Random walks in random scenery are processes defined by , where and are two independent sequences of i.i.…

math.PR2011★ 4 cited

A crossover for the bad configurations of random walk in random scenery

Sébastien Blachère, Frank den Hollander, Jeffrey E. Steif

In this paper, we consider a random walk and a random color scenery on Z. The increments of the walk and the colors of the scenery are assumed to be i.i.d. and to be independent of…

math.PR2011★ 5 cited

K-independent percolation on trees

Pierre Mathieu, Christoph Temmel

Consider the class of k-independent bond, respectively site, percolations with parameter p on an infinite tree T. We derive tight bounds on p for both a.s. percolation and a.s. non…