Applications of large deviation theory of Markov Processes: imitation of big fluctuations in physical models

Abstract

The large deviation theory is one of the well developed and currently applied parts of the probability theory. The goal of this project is an application of the large deviation theory to continuous time Markov processes.The studied models subjected to the Markov dynamics that has, in general, the following structure. There exist a finite number of particles, every particle is supplied by a space of spins, the same for all particles. In this project, the spin state is a subset of the real line. The Markov process is realized as a random change of the spin value at a randomly chosen particle. It means we consider the jump-wise Markov processes with continuous time. The negative spin jumps are called emissions, and the positive spin jumps are called excitations. The emission is when a spin value at some particle is changed to a lower value, the excitation is when the change has opposite direction.One of our interests in the studies concerns the big fluctuation of the emission on a finite time interval.We are going to apply the method to investigate the large fluctuations of Hawking-Penrose black hole models. (AU)