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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2019

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’.
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Dates et versions

hal-02122803 , version 1 (11-01-2024)

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Cecile Monthus. Large deviations for dynamical fluctuations of open Markov processes, with application to random cascades on trees. Journal of Physics A: Mathematical and Theoretical, 2019, 52 (2), pp.025001. ⟨10.1088/1751-8121/aaf141⟩. ⟨hal-02122803⟩
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