33 citations · 105 across the 13 of their papers we have counts for
16 papers · 1 filter
Are random random walks normal?
Kais Hamza, Laurent Tournier
Given a symmetric simple random walk , the family of all symmetric simple random walks adapted to the filtration of was studied…
Combinatorial universality in three-speed ballistic annihilation
John Haslegrave, Laurent Tournier
We consider a one-dimensional system of particles, moving at constant velocities chosen independently according to a symmetric distribution on , and annihilating upon…
A deterministic walk on the randomly oriented Manhattan lattice
Andrea Collevecchio, Kais Hamza, Laurent Tournier
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping indep…
Three-speed ballistic annihilation: phase transition and universality
John Haslegrave, Vladas Sidoravicius, Laurent Tournier
We consider ballistic annihilation, a model for chemical reactions first introduced in the 1980's physics literature. In this particle system, initial locations are given by a rene…
The ballistic annihilation threshold is 1/4
Vladas Sidoravicius, Laurent Tournier
We consider a system of annihilating particles where particles start from the points of a Poisson process on the line, move at constant i.i.d. speeds symmetrically distributed in {…
Uniqueness of the infinite noodle
Nicolas Curien, Gady Kozma, Vladas Sidoravicius +1
Consider the graph obtained by superposition of an independent pair of uniform infinite non-crossing perfect matchings of the set of integers. We prove that this graph contains at…
Note on a one-dimensional system of annihilating particles
Vladas Sidoravicius, Laurent Tournier
We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d.…
Random walks in Dirichlet environment: an overview
Christophe Sabot, Laurent Tournier
Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on where the transition probabilities are i.i.d. at each site with…
Non-fixation for Biased Activated Random Walks
Leonardo T. Rolla, Laurent Tournier
We prove that the model of Activated Random Walks on Z^d with biased jump distribution does not fixate for any positive density, if the sleep rate is small enough, as well as for a…
Greedy Clearing of Persistent Poissonian Dust
Leonardo T. Rolla, Vladas Sidoravicius, Laurent Tournier
Given a Poisson point process on R, assign either one or two marks to each point of this process, independently of the others. We study the motion of a particle that jumps determin…
Asymptotic direction of random walks in Dirichlet environment
Laurent Tournier
In this paper we generalize the result of directional transience from [SabotTournier10]. This enables us, by means of [Simenhaus07], [ZernerMerkl01] and [Bouchet12] to conclude tha…
Quenched limits for the fluctuations of transient random walks in random environment on Z
Nathanaël Enriquez, Christophe Sabot, Laurent Tournier +1
We consider transient nearest-neighbor random walks in random environment on Z. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe…
Stable fluctuations for ballistic random walks in random environment on Z
Nathanaël Enriquez, Christophe Sabot, Laurent Tournier +1
We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer pr…
A note on the recurrence of edge reinforced random walks
Laurent Tournier
We give a short proof of Theorem 2.1 from [MR07], stating that the linearly edge reinforced random walk (ERRW) on a locally finite graph is recurrent if and only if it returns to i…
Reversed Dirichlet environment and directional transience of random walks in Dirichlet random environment
Christophe Sabot, Laurent Tournier
We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^…
Integrability of exit times and ballisticity for random walks in Dirichlet environment
Laurent Tournier
We consider random walks in Dirichlet environment, introduced by Enriquez and Sabot in 2006. As this distribution on environments is not uniformly elliptic, the annealed integrabil…