Large deviations conditioned on large deviations I: Markov chain and Langevin equation

Nonequilibrium Markov Processes Conditioned on Large Deviations

Large Deviations for Langevin

We study the asymptotic behavior of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum...

Stochastic gene expression conditioned on large deviations.

The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare events motivates the analysis of large deviations in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics have l...

Multiplicative Ergodicity and Large Deviations for an Irreducible Markov Chain∗

The paper examines multiplicative ergodic theorems and the related multiplicative Poisson equation for an irreducible Markov chain on a countable state space. The partial products are considered for a realvalued function on the state space. If the function of interest satisfies a monotone condition, or is dominated by such a function, then (i) The mean normalized products converge geometrically...

Large Deviations