Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates

Cecile Monthus

Published 2021-03-16Version 1

One-dimensional run-and-tumble processes may converge towards some localized steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the large deviations at Level 2.5 for the joint probability of the empirical densities, of the empirical spatial currents and of the empirical switching flows. The scaled cumulant generating function of general time-additive observables can be obtained via contraction from the Level 2.5, or equivalently via the deformed generator method and the corresponding Doob conditioned process. Finally, the large deviations for the empirical intervals between consecutive switching events can be derived via the introduction of the alternate Markov chain that governs the series of all the switching events of a long trajectory.