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Gibbs Measures and Phase Transitions on Sparse Random Graphs
Random graphs Ising model Gibbs measures Phase transitions Spin models Local weak convergence
2015/8/20
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sp...
Developments in perfect simulation for Gibbs measures
Perfect Simulation Stochastic Order Gibbs Measures
2011/8/30
Abstract: This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are l...
On invariant Gibbs measures conditioned on mass and momentum
Gibbs measure Schr¨odinger equation Kortweg-de Vries equation
2011/2/21
We construct a Gibbs measure for the nonlinear Schr¨odinger equation (NLS)on the circle, conditioned on prescribed mass and momentum:dμa,b = Z−1 1 {´T |u|2=a} 1 {i ´T uux=b}e±1
p &a...
Spectral metric spaces for Gibbs measures
Noncommutative Geometry Spectral Triple Entropy Gibbs Measure
2011/2/25
We construct spectral metric spaces for Gibbs measures on a onesided topologically exact subshift of finite type. That is, for a given Gibbs measure we construct a spectral triple and show that Connes...
The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices
The q-Gelfand-Tsetlin graph Gibbs measures
2010/11/12
The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive...
Analytic properties of fractional Schrödinger semigroups and Gibbs measures for symmetric stable processes
Schrö dinger semigroups Gibbs measures symmetric stable processes
2010/11/18
We establish a Feynman-Kac-type formula to define fractional Schr\"odinger operators for fractional Kato-decomposable potentials as self-adjoint operators. In this functional integral representation ...
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
2010/12/14
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...
In this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of Ha...