Related papers: Condenser physics applied to Markov chains - A bri…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
We trace the history of empirical entropy, touching briefly on its relation to Markov processes, normal numbers, Shannon entropy, the Chomsky hierarchy, Kolmogorov complexity, Ziv-Lempel compression, de Bruijn sequences and stochastic…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
In this paper, first-passage probability of Markov chains is used to get a strict proof of the existence of degree distribution of the LCD model presented by Bollobas (Random Structures and Algorithms 18(2001)). Also, a precise expression…
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…
This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes…
This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.
I study how to apply relativistic quantum field theory to condensed matter systems. The motivation for this is examined and then two separate elements are considered. First we identify the precise relationship between relativistic and…
We proposed in \cite{bl2} a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible dynamics based on the Dirichlet…
These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of…
The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.