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Kinetically constrained models (KCMs) are interacting particle systems on $Z^d$ with a continuous-time constrained Glauber dynamics, which were introduced by physicists to model the liquid-glass transition. One of the most well-known KCMs…
We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density $q$ of facilitating sites in the equilibrium measure (but not necessarily in the initial measure) is…
We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics…
Kinetically constrained models (KCMs) have been used to study and understand the origin of glassy dynamics. Despite having trivial thermodynamic properties, their dynamics slows down dramatically at low temperatures while displaying…
In this chapter we summarize recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which we cover we study the possible occurrence of ergodicity…
Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb{Z}^d$ with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with…
Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of…
Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish non-perturbative constraints on the…
Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In…
We analyze the relaxation to equilibrium for kinetically constrained spin models (KCSM) when the initial distribution $\nu$ is different from the reversible one, $\mu$. This setting has been intensively studied in the physics literature to…
Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their…
Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of…
We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the non-equilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a…
We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical…
Dense liquids gradually transform into non-equilibrium amorphous solids as they pass through the experimental glass transition. Experimentally, ergodicity is lost because measurements are conducted within a finite time window. More than…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
The bisection method for kinetically constrained models (KCM) of Cancrini, Martinelli, Roberto and Toninelli is a vital technique applied also beyond KCM. In this note we present a new way of performing it, based on a novel two-block…
We prove that any subcritical solution to the Becker-D\"{o}ring equations converges exponentially fast to the unique steady state with same mass. Our convergence result is quantitative and we show that the rate of exponential decay is…
This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…