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Related papers: Regular $g$-measures are not always Gibbsian

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The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…

History and Philosophy of Physics · Physics 2018-08-07 Simon Saunders

It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy…

Statistical Mechanics · Physics 2007-05-23 C. Maes

We construct Gibbs perturbations of the Gamma process on $\mathbbm{R}^d$, which may be used in applications to model systems of densely distributed particles. First we propose a definition of Gibbs measures over the cone of discrete Radon…

Mathematical Physics · Physics 2012-07-13 Dennis Hagedorn , Yuri Kondratiev , Tanja Pasurek , Michael Röckner

A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact…

Artificial Intelligence · Computer Science 2012-06-18 Tal El-Hay , Nir Friedman , Raz Kupferman

In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) {\em From}…

Mathematical Physics · Physics 2015-06-26 A. C. D. van Enter , C. Kuelske

Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…

Systems and Control · Electrical Eng. & Systems 2023-11-30 Jilles van Hulst , Roy van Zuijlen , Duarte Antunes , W. P. M. H. , Heemels

A sufficient condition for the Gibbs states of a shift-invariant specification on a one-dimensional lattice to be the $g$-chains for some continuous function $g$ is obtained. This is then used to derive criteria under which there is a…

Dynamical Systems · Mathematics 2025-04-23 Paul Hulse

This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…

Probability · Mathematics 2010-08-23 Hana Kogan , Michael B. Marcus , Jay Rosen

We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter dynamic, and a coalescing particle model. In each of the…

Probability · Mathematics 2024-05-20 Piet Lammers , Fabio Toninelli

A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism…

Methodology · Statistics 2020-09-24 Eric J Tchetgen Tchetgen , Andrew Ying , Yifan Cui , Xu Shi , Wang Miao

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamical formalism for generalized Gibbs states will be discussed. A new class of…

Mathematical Physics · Physics 2007-05-23 A. C. D. van Enter , E. A. Verbitskiy

It was shown many times in the literature that a Markov random field is equivalent to a Gibbs random field when all realizations of the field have non-zero probabilities; the proofs are rather complicated. A simpler proof, which is based…

Probability · Mathematics 2016-03-07 Levent Onural

For every $p>2$, we construct a regular and continuous specification ($g$-function), which has a variation sequence that is in $l^p$ and which admits multiple Gibbs measures. Combined with a recent result of Johansson and Oberg, this…

Probability · Mathematics 2007-05-23 Noam Berger , Christopher Hoffman , Vladas Sidoravicius

Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of atmospheric carbon dioxide levels. Notably, the choice of GP kernel is often somewhat arbitrary. In particular,…

How an economic agent (a firm, an investor or a financial market) evaluates a contingent claim, say a European type of derivatives X, with maturity t? In this paper we study a mechanism of dynamic expectations and evaluations. We give the…

Probability · Mathematics 2007-05-23 Shi-Ge Peng

The Gibbs sampler (GS) is a crucial algorithm for approximating complex calculations, and it is justified by Markov chain theory, the alternating projection theorem, and $I$-projection, separately. We explore the equivalence between these…

Computation · Statistics 2024-10-15 Kun-Lin Kuo , Yuchung J. Wang

We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…

Methodology · Statistics 2025-09-23 Patrick Bastian , Tim Kutta , Rupsa Basu , Holger Dette

We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…

Mathematical Physics · Physics 2018-09-26 Rodrigo Bissacot , Eric Ossami Endo , Aernout C. D. van Enter , Arnaud Le Ny

Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. We establish a connection between the invariance of Gibbs measures and the…

Dynamical Systems · Mathematics 2015-05-15 Jarkko Kari , Siamak Taati

We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…

Probability · Mathematics 2022-07-15 Sylvie Roelly , Alexander Zass