Displaying similar documents to “First-passage competition with different speeds: positive density for both species is impossible.”

Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley (2010)

ESAIM: Probability and Statistics

Similarity:

We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths. ...

Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster

Olivier Garet, Régine Marchand (2004)

ESAIM: Probability and Statistics

Similarity:

The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on d to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet vertices to a deterministic shape that does not depend on the realization of the infinite cluster. As a special case of our result, we obtain an asymptotic shape theorem for the chemical distance...