The random average process is a randomly evolving d-dimensional surface whose heights are updated by random convex combinations of neighboring heights. The !uctuations of this process in case of linear initial conditions ...

We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2 <= a <= M <= infinity. Particles move independently as continuous time simple ...

We construct an infinite volume spatial random permutation (χ,σ), where χ⊂ℝd is a point process and σ:χ→χ is a permutation (bijection), associated to the formal Hamiltonian H(χ,σ)=∑_x∈χ‖x−σ(x)‖2. The measures are parametrized ...

We consider a random walk in random environment in the low disorder regime on Zd. That is, the probability that the random walk jumps from a site x to a nearest neighboring site x+e is given by p(e)+ǫξ(x,e), where p(e) is ...

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes ...

By constructing jointly a random graph and an associated exploration process, we define the dynamics of a “parking process” on a class of uniform random graphs as a measure-valued Markov process, representing the empirical ...