Distribution of Time-Averaged Observables for Weak Ergodicity Breaking

Distribution of time-averaged observables for weak ergodicity breaking.

We find a general formula for the distribution of time-averaged observables for systems modeled according to the subdiffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly nonergodic statistical mechanical framework is constructed, which is based on Lévy's gene...

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

on $l_1$-weak ergodicity of nonhomogeneous continuous-time markov‎ ‎processes

‎in the present paper we investigate the $l_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time markov processes with general state‎ ‎spaces‎. ‎we provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $l_1$-weak ergodicity‎. ‎moreover‎, ‎we apply‎ ‎the obtained results to establish $l_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Distribution of population-averaged observables in stochastic gene expression.

Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population-averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population-averag...

Weak-ergodicity Breaking in Mean-field Spin-glass Models