The classical limit of reduced quantum stochastic evolutions
The continuum reaction-diffusion limit of a stochastic cellular growth model
A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered....
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
The escape model on a homogeneous tree.
The foundations of probability with black swans.
The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...
The incipient infinite cluster in high-dimensional percolation.
The jammed phase of the Biham-Middleton-Levine traffic model.
The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.
The large-scale limit of Dyson's hierarchical vector valued model at low temperatures. The non-gaussian case. Part I : limit theorem for the average spin
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit
The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
The longtime behavior of branching random walk in a catalytic medium.
The Markov process of total spins
The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary
The metastability threshold for modified bootstrap percolation in dimensions.
The ODE method for some self-interacting diffusions on ℝd
The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝd. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure μt. These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝd, assuming a confinement potential satisfying some conditions. These hypotheses on the confinement...
The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent
In this paper we study the parabolic Anderson equation , , , where the -field and the -field are -valued, is the diffusion constant, and is the discrete Laplacian. The -field plays the role of adynamic random environmentthat drives the equation. The initial condition , , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump...
The parabolic-parabolic Keller-Segel equation
I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].
The posterior metric and the goodness of gibbsianness for transforms of Gibbs measures.