Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model

TL;DR

This paper investigates the large deviation properties of local empirical densities and activities in the East model, revealing anomalous fluctuations and phase transition-like singularities in the pure and random versions, which vanish under soft constraints.

Contribution

It introduces a large deviations framework focusing on local empirical densities and activities, providing new insights into the dynamical anomalies of the East model and its variants.

Findings

Revealed anomalous large deviations and phase transition-like singularities in the East model.

Characterized the rate functions for local empirical densities and activities.

Showed that these singularities disappear with soft constraints.

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 various levels for the relevant local empirical densities and activities that only involve two consecutive spins. This framework allows to characterize their anomalous rate functions and to analyze the consequences for all the time-additive observables that can be reconstructed from them, both for the pure and for the random East model. These singularities in dynamical large deviations properties disappear when the hard-constraint of the East model is replaced by the soft constraint.