Percolation and first-passage percolation on oriented graphs

The key step to recover a full limit from the limit of a random subsequence is the continuity lemma 4.2: using the coupled zone, we prove in essence that two points close in Z d × N

The next result says that the mutual unbounded growth in the two-type first- passage percolation model and the existence of two distinct semi-infinite geodesics in the embedded

We first discuss generalizations of the oriented bond percolation model that do not require any change in our proof of the main results, then we consider oriented site percolation

We pursue the study of a random coloring first passage percolation model introduced by Fontes and Newman.. We prove that the asymptotic shape of this first passage percolation

Boboc, Excessive functions and excessive measures: Hunt’s theorem on balayages, quasi-continuity.. Worpshop Classical and Modern Potential Theory and Appl., NATO ASI Series C

We will first study two particular cases of this result in the model of Bernoulli percolation, that will allow us to deal very simply with the proof of the main theorem in general

Although this method to employ type II sums on questions about prime number asymptotics is somewhat easier than those already in the literature, it seems harder to incorporate

The history of previous attempts to obtain a stronger result than Siegers is a curious chapter of accidents, and will be briefly summarised here before