2021
DOI: 10.48550/arxiv.2109.05924
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Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model

Cecile Monthus

Abstract: The East model is the simplest one-dimensional kinetically-constrained model of N spins with a trivial equilibrium that displays anomalously large spatio-temporal fluctuations, with characteristic "space-time bubbles" in trajectory space, and with a discontinuity at the origin for the first derivative of the scaled cumulant generating function of the total activity. These striking dynamical properties are revisited via the large deviations at Level 2.5 for the relevant local empirical densities and flows that … Show more

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Cited by 2 publications
(5 citation statements)
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“…x y =x q(x, y) ln q(x, y) w x,y ρ(y) − q(x, y) + w x,y ρ(y) (47) This rate function characterizes how rare it is for large T to see some empirical density ρ(.) and some empirical flows q(., .)…”
Section: Reminder On the Large Deviations At Level 25 For The Time-av...mentioning
confidence: 99%
“…x y =x q(x, y) ln q(x, y) w x,y ρ(y) − q(x, y) + w x,y ρ(y) (47) This rate function characterizes how rare it is for large T to see some empirical density ρ(.) and some empirical flows q(., .)…”
Section: Reminder On the Large Deviations At Level 25 For The Time-av...mentioning
confidence: 99%
“…In this section, we follow the approach that has recently been applied to the kineticallyconstrained East model [27] in order to identify the appropriate local empirical observables and to analyze whether it is possible to write closed large deviations properties for them.…”
Section: Analysis Of the Relevant Local Empirical Time-averaged Obser...mentioning
confidence: 99%
“…For a given Markov model, the relevant time-empirical observables are defined as the time-empirical observables that determine the trajectories probabilities (see appendix A of [27] for a general discussion). For the present Markov jump process, the probability of equation (A3) for the trajectory C(t) = {S 1 (t), .…”
Section: Identification Of the Relevant Time-empirical Observables Th...mentioning
confidence: 99%
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