Large deviations for dynamical fluctuations of open Markov processes, with application to random cascades on trees
Résumé
The large deviations at ’Level 2.5 in time’ for time-dependent ensemble-empirical-observables,
introduced by C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] for
the case of N independent Markov jump processes, are extended to the case of open Markov processes
with reservoirs : explicit formulas are given for the joint probability of empirical occupation numbers
and empirical flows, both for discrete-time dynamics and for continuous-time jump dynamics, with
possibly time-dependent dynamical rules and/or time-dependent driving of the reservoirs. This
general formalism is then applied to random cascades on trees, where particles are injected at the
root via a ’source reservoir’, while the particles are removed at the leaves of the last generation of
the tree via ’sink reservoirs’.
Domaines
Physique [physics]
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