Comportement asymptotique d'un système infini de particules additif sur Z
Comportement hydrodynamique et entropie relative des processus de sauts, de naissances et de morts
Confinement of the two dimensional discrete Gaussian free field between two hard walls.
Connectivity bounds for the vacant set of random interlacements
The model of random interlacements on ℤd, d≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter u parametrizes the density of random interlacements on ℤd. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level u, in the non-percolative regime u>u∗, with u∗ the non-degenerate critical parameter for the percolation...
Constructing quantum dissipations and their reversible states from classical interacting spin systems
Controlling Griffiths' singularities
Convergence of a “Gibbs-Boltzmann” random measure for a typed branching diffusion
Convergence of coalescing nonsimple random walks to the Brownian web.
Convergence of critical oriented percolation to super-brownian motion above dimensions
Convergence of lattice trees to super-Brownian motion above the critical dimension.
Convergence of simple random walks on random discrete trees to brownian motion on the continuum random tree
In this article it is shown that the brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete n-vertex ordered graph trees whose search-depth functions converge to the brownian excursion as n→∞. We prove both a quenched version (for typical realisations of the trees) and an annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random walks...
Convergence results and sharp estimates for the voter model interfaces.
Convergence to the brownian Web for a generalization of the drainage network model
We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.
Convex entropy decay via the Bochner–Bakry–Emery approach
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...
Copolymer at selective interfaces and pinning potentials : weak coupling limits
We consider a simple random walk of length N, denoted by (Si)i∈{1, …, N}, and we define (wi)i≥1 a sequence of centered i.i.d. random variables. For K∈ℕ we define ((γi−K, …, γiK))i≥1 an i.i.d sequence of random vectors. We set β∈ℝ, λ≥0 and h≥0, and transform the measure on the set of random walk trajectories with the hamiltonian λ∑i=1N(wi+h)sign(Si)+β∑j=−KK∑i=1Nγij1{Si=j}. This transformed path measure describes an hydrophobic(philic) copolymer interacting with a layer of width 2K around an interface...
Coupled map lattices with asynchronous updatings
Couplings, attractiveness and hydrodynamics for conservative particle systems
Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived markovian coupled process (ξt, ζt)t≥0 satisfies: (A) if ξ0≤ζ0 (coordinate-wise), then for all t≥0, ξt≤ζt a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on ℤd such that, in each transition, k particles may jump from a site x to another site y,...
Critical exponents in percolation via lattice animals.
Critical path analysis for continuum percolation
Critical percolation on certain nonunimodular graphs.