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- P. Caputo, Y. Velenik
- 2000

We prove existence of a wetting transition for two classes of gradient elds which include: (1) The Continuous SOS model in any dimension and (2) The massless Gaussian model in dimension 2. Combined with a recent result proving the absence of such a transition for Gaussian models above 2 dimensions (Bolthausen et al., 2000. J. Math. Phys. to appear), this… (More)

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)

- PIETRO CAPUTO
- 2003

Abstract. 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. 2000 MSC: 60K35

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)

- PIETRO CAPUTO
- 2003

– Consider uniformly elliptic random walk on Z 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. 2003 Éditions scientifiques et médicales Elsevier SAS MSC: 60K37; 60K35;… (More)

- N Cancrini, P Caputo, F Martinelli
- 2006

We prove tight bounds on the relaxation time of the so called L– reversal chain, introduced by R. Durrett as a stochastic model for the evolution of chromosome chains. The process is described as follows: we have n distinct letters on the vertices of the n–cycle (Z mod n); at each step a connected subset of the graph is chosen uniformly at random among all… (More)

- PIETRO CAPUTO, HUBERT LACOIN, FABIO MARTINELLI, FABIO LUCIO TONINELLI
- 2012

We consider the stochastic evolution of a (1 + 1)-dimensional polymer in the depinned regime. At equilibrium the system exhibits a double well structure: the polymer lies (essentially) either above or below the repulsive line. As a consequence, one expects a metastable behavior with rare jumps between the two phases combined with a fast thermalization… (More)

- P Caputo, A Faggionato, T Prescott
- 2012

We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the α-power of the jump length and depend on the energy marks via a Boltzmann–like factor. The case α = 1 corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization.… (More)

- Pietro Caputo
- 2008

We give a new and elementary computation of the spectral gap of the Kac walk on S . The result is obtained as a by–product of a more general observation which allows to reduce the analysis of the spectral gap of an N–component system to that of the same system for N = 3. The method applies to a number of random “binary collision” processes with… (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)