Related papers: Stochastic dynamics for Group Field Theories
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
We establish a connection between the structure of a stationary symmetric alpha-stable random field (0 < alpha < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosinski (2000). With the help of this…
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium…
We will construct a theory which can explain the dynamics toward the steady state self-gravitating systems (SGSs) where many particles interact via the gravitational force. Real examples of SGS in the universe are globular clusters and…
In this paper, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description to phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz…
We propose a mechanism naturally leading to the spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a non zero chemical potential to one of the globally…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
In a previous study we developed a mean-field theory of dynamical transitions for the totally-asymmetric simple-exclusion process (TASEP) with open boundaries and Langmuir kinetics, in the so-called balanced regime, characterized by equal…
Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations…
The dynamics of the Hamiltonian mean field model is studied in the context of continuous time random walks. We show that the sojourn times in cells in the momentum space are well described by a L\'evy truncated distribution. Consequently…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…
We present a comprehensive study of phase transitions in single-field systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is…
We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…
We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different…