Related papers: Gibbs measures on Subshifts

Given n independent Bernoulli(p) random variables X_i, i = 1, ..., n, representing the opinions of individuals connected by an underlying random k-regular graph G_n on {1, ..., n}, we show that when conditioned on an atypical empirical…

Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…

We prove inequalities relating the measures of maximal entropy of two patterns u,v where the extender set of u is contained in the extender set of v. Our main results are two generalizations of a Theorem of Meyerovitch; the first applies to…

Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

Let $\mu$ be a Gibbs measure of the doubling map $T$ of the circle. For a $\mu$-generic point $x$ and a given sequence $\{r_n\} \subset \R^+$, consider the intervals $(T^nx - r_n \pmod 1, T^nx + r_n \pmod 1)$. In analogy to the classical…

Geometric models and Teichm\"uller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one…

We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.

We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In…

This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which…

In this work, we model the temperature measurement as a transformation of the arbitrary state into the Gibbs state. We start with a general formalism of ansatz-posteriors, which includes many usual models of posterior states due to…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic…

The variational principle for Gibbs point processes with general finite range interaction is proved. Namely, the Gibbs point processes are identified as the minimizers of the free excess energy equals to the sum of the specific entropy and…

There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…

We consider disordered lattice spin models with finite volume Gibbs measures $\mu_{\L}[\eta](d\s)$. Here $\s$ denotes a lattice spin-variable and $\eta$ a lattice random variable with product distribution $\P$ describing the disorder of the…

This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this…

In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In…

We consider skew products over subshifts of finite type in which the fibers are copies of the real line, and we study their mixing properties with respect to any infinite invariant measure given by the product of a Gibbs measure on the base…

In this paper, we consider which kind of invariant measure on hereditary subshifts is not Gibbs measure. For the hereditary closure of a subshift $(X,S)$, we prove that in some situation, the invariant measure $\nu*B_{p,1-p}$ can not be a…