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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)
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)
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)