Applications of large deviation theory of Markov Processes: imitation of big fluct...
| Grant number: | 11/21089-4 |
| Support type: | Research Grants - Visiting Researcher Grant - International |
| Duration: | March 10, 2012 - June 10, 2012 |
| Field of knowledge: | Physical Sciences and Mathematics - Probability and Statistics - Probability |
| Principal Investigator: | Serguei Popov |
| Grantee: | Serguei Popov |
| Visiting researcher: | Gunter Markus Schutz |
| Visiting researcher institution: | Forschungszentrum Jülich, Germany |
| Home Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
| Associated research grant: | 09/52379-8 - Stochastic modeling of interacting systems, AP.TEM |
Abstract
We study the microscopic large deviation properties of the ASEP with random rates, i.e. the microscopic space-time structure of this process for atypical currents. For the case of a small number of particles in the infinite lattice we shall study scaling solutions, ergodicity and mean first passage times for an associated generalized random walk similar to the Lamperti problem. In the many-particle case on a finite lattice we shall obtain the current cumulants for a quasi-conservative system conditioned on the absence of particle annihilation. In the disordered case conditioned on an atypically high current we shall construct the generator of an effective process with long-range interactions whose invariant measure is the quasi-stationary measure in the large deviation regime. We address the question whether there is a condensation transition and also what the most likely distribution of distances between particles is. (AU)