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arXiv · 1808.09703

Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees

Cecile Monthus
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Abstract

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'.

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Cecile Monthus. 2018-08-29. Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees. https://doi.org/10.1088/1751-8121/aaf141

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