Large deviations of the current in stochastic collisional dynamics

Abstract

We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by the Green-Kubo relation. Next we show that the law of the empirical average current satisfies a large deviations principle and compute explicitly the rate functional in a suitable scaling limit. We observe that this functional is not strictly convex.

keywords and references added

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Cited by in corpus (11)

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• Large-time asymptotic of heavy tailed renewal processes
• Work fluctuations for a confined Brownian particle: the role of initial conditions
• Donsker-Varadhan asymptotics for degenerate jump Markov processes
• Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions