Rare event statistics in reaction-diffusion systems

Rare event statistics in reaction-diffusion systems.

We present an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction-diffusion systems. This method is based on a semiclassical treatment of an underlying "quantum" Hamiltonian, encoding the system's evolution. To this end, we formulate the corresponding canonical dynamical system and investigate its phase portrait. This method is pre...

Spectral formulation and WKB approximation for rare-event statistics in reaction systems.

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. We compare the stationary WKB approximation to a recent time-dependent semiclassical approximation developed, for the same class of problems, by E...

Estimation of Rare Event Statistics in Data

The estimation of the statistics of rare events is inherently costly, simply because of their rarity. This paper describes some recently developed techniques for the efficient simulation of rare events in telecommunications networks. The work described is split into three broad themes: the optimal simulation of buffer overflows in queueing networks, reverse-time modeling of random processes and...

Reaction Event Counting Statistics of Biopolymer Reaction Systems with Dynamic Heterogeneity.

We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we f...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems