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Consider uniformly elliptic random walk on Z d with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized effective diffusion matrices.
We prove a uniform Poincaré inequality for non–interacting unbounded spin systems with a conservation law, when the single–site potential is a bounded perturbation of a convex function with polynomial growth at infinity. The result is then applied to Ginzburg-Landau processes to show diffusive scaling of the associated spectral gap.
Aldous' spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The novelty is an idea based… (More)
We prove new inequalities implying exponential decay of relative entropy functionals for a class of Zero–Range processes on the complete graph. We first consider the case of uniformly increasing rates, where we use a discrete version of the Bakry– Emery criterium to prove spectral gap and entropy dissipation estimates, uniformly over the number of particles… (More)
Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diffusions on the lattice, we consider an anisotropic simple exclusion process with N particles in a rectangle of Z 2. Every particle at row h tries to jump to an arbitrary empty site at row h ± 1 with rate q ±1 , where q ∈ (0, 1) is a measure of the… (More)
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n + 1)/2 edges of the graph and normalizing each weight by the corresponding row sum. We have already shown in a previous work that if L has finite second moment then, as n goes to infinity, the limiting… (More)
The paper concerns lattice triangulations, i.e., triangulations of the integer points in a polygon in R<sup>2</sup> whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects in their own right and by virtue of applications in algebraic geometry. Our focus is on random triangulations in which a… (More)
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior at the edge, including the so called spectral gap. Results are obtained for two simple models with distinct limiting… (More)
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both the almost sure global behavior of the spectrum , and the local behavior at the edge including the so called spectral gap. We study presently two simple models.… (More)
We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We prove various estimates on the low-temperature behavior which confirm and extend previous work by physicists. 1.… (More)