14 citations · 26 across the 7 of their papers we have counts for
7 papers
Self-organized criticality in a discrete model for Smoluchowski's equation with limited aggregations
Mathieu Merle, Raoul Normand
We introduce and study a discrete random model for Smoluchowski's equation with limited aggregations. The latter is a model of coagulation introduced by Bertoin which may exhibit g…
Self-organized criticality in a discrete model for Smoluchowski's equation
Mathieu Merle, Raoul Normand
We study a discrete model of coagulation, involving a large number of particles. Pairs of particles are given i.i.d exponential clocks with parameter . When a clock rings,…
Weak noise and non-hyperbolic unstable fixed points: Sharp estimates on transit and exit times
Giambattista Giacomin, Mathieu Merle
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance . When such equations…
Scaling limit of the invasion percolation cluster on a regular tree
Omer Angel, Jesse Goodman, Mathieu Merle
We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height funct…
A random walk on Z with drift driven by its occupation time at zero
Iddo Ben-Ari, Mathieu Merle, Alexander Roitershtein
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of…
Probability of hitting a distant point for the voter model started with a single one
Mathieu Merle
The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In…