Publication

Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces

Charles Pfister
2020
Journal Articles

Abstract

For the spaceXin a large class of finite alphabet shift spaces (lattice models) and the class of functionsfwith bounded total oscillations, we prove that each equilibrium measure nu atf=phi is a weak Gibbs measures for phi-P(phi). In addition, the empirical measures satisfy a full large deviations principle for (X,nu).

Official source

https://infoscience.epfl.ch/entities/publication/f77fe13c-cafb-4d87-8a39-1bc50e7b4f05

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Charles Pfister
2020
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/f77fe13c-cafb-4d87-8a39-1bc50e7b4f05

About this result

Related concepts (11)

Lattice model (physics)

In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory.

Subshift of finite type

In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state machine. The most widely studied shift spaces are the subshifts of finite type. Let V be a finite set of n symbols (alphabet). Let X denote the set V^\Z of all bi-infinite sequences of elements of V together with the shift operator T. We endow V with the discrete topology and X with the product topology.

Ising model

The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.

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Iop Publishing Ltd2024