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...