Full-counting statistics of random transition-rate matrices

Abstract

We study the full counting statistics of current of large open systems through the application of random matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.

Genetic noise mechanism for power-law switching in bacterial flagellar motors

“…Costly numerical sampling can be avoided by implementing the toolbox of full-counting statistics [23]. Originally introduced in the context of quantum transport [24], this formalism applies to all master equations, independent of their genesis [25]. Here we demonstrate how it can be used to extract switching statistics directly from transition rates K ± x (Y) and K ± y (Y ).…”

“…This probability is specific to the initial distribution P entry ≡ {P entry (Y )}, P entry (Y ) := P (1, Y, 0) (the meaning of this notation will be apparent soon). For a chosen initial state, P(t) can be calculated from the state vector P (0) (t) ≡ {P (0) (Y ; t)} (here superscript (0) denotes number of transitions on which the state is conditioned [25]). The evolution of this vector is governed by the master equationṖ…”

On photon statistics parametrized by a non-central Wishart random matrix

“…), then cumulants are the coefficients of log(M (t)) and factorial cumulants are the coefficients of log(M (log(1 + t))). Cumulants have special properties and if some of these properties can be deduced from data, then special stochastic models can be inferred [19]. For example, if conditioned cumulants linearize, then the recorded data can be modeled by using (1.1).…”