Relaxation in infinite spin systems
Remarks on intersection-equivalence and capacity-equivalence
Remarks on the life and research of Roland L. Dobrushin.
Renewal convergence rates and correlation decay for homogeneous pinning models.
Renormalizations of branching random walks in equilibrium.
Representation theorems for interacting Moran models, interacting Fisher-Wright diffusions and applications.
Repulsion of an evolving surface on walls with random heights
Return probabilities of a simple random walk on percolation clusters.
Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment
We consider random walks in a random environment given by i.i.d. Dirichlet distributions at each vertex of ℤd or, equivalently, oriented edge reinforced random walks on ℤd. The parameters of the distribution are a 2d-uplet of positive real numbers indexed by the unit vectors of ℤd. We prove that, as soon as these weights are nonsymmetric, the random walk is transient in a direction (i.e., it satisfies Xn ⋅ ℓ →n +∞ for some ℓ) with positive probability. In dimension 2, this result is strenghened...
Scale-free percolation
We formulate and study a model for inhomogeneous long-range percolation on . Each vertex is assigned a non-negative weight , where are i.i.d. random variables. Conditionally on the weights, and given two parameters , the edges are independent and the probability that there is an edge between and is given by . The parameter is the percolation parameter, while describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...
Scaling limit and cube-root fluctuations in SOS surfaces above a wall
Consider the classical -dimensional Solid-On-Solid model above a hard wall on an box of . The model describes a crystal surface by assigning a non-negative integer height to each site in the box and 0 heights to its boundary. The probability of a surface configuration is proportional to , where is the inverse-temperature and sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough temperatures....
Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation.
Scaling limits of anisotropic Hastings–Levitov clusters
We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Second class particles in the rarefaction fan
Self Diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion
Self-dual planar hypergraphs and exact bond percolation thresholds.
Self-interacting diffusions II : convergence in law
Seuils de percolation en dimension deux
Shape transition under excess self-intersections for transient random walk
We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.