A note on the Fredrickson-Andersen one spin facilitated model in stationarity

Time Scales of the Fredrickson-Andersen Model on Polluted $\mathbb{Z}^{2}$ and $\mathbb{Z}^{3}$

We study the Kinetically Constrained Model on the polluted square lattice, with two-neighbor constraints. For a quenched polluted environment with low pollution density we give bounds on the infection time of the origin.

Cutoff for the Fredrickson-Andersen one spin facilitated model

The Fredrickson-Andersen one spin facilitated model belongs to the class of Kinetically Constrained Spin Models. It is a non attractive process with positive spectral gap. In this paper we give a precise result on the relaxation for this process on an interval $[1,L]$ starting from any initial configuration. A consequence of this result is that this process exhibits cutoff at time $L/(2v)$ with window $O(\sqrt{L})$ for a certain positive constant $v$. The key ingredient is the study of the evolution of the leftmost empty site in a filled infinite half-line called the front. In the process of t…

Front evolution of the Fredrickson-Andersen one spin facilitated model

The Fredrickson-Andersen one spin facilitated model (FA-1f) on Z belongs to the class of kinetically constrained spin models (KCM). Each site refreshes with rate one its occupation variable to empty (respectively occupied) with probability q (respectively $p = 1 - q$), provided at least one nearest neighbor is empty. Here, we study the non equilibrium dynamics of FA-1f started from a configuration entirely occupied on the left half-line and focus on the evolution of the front, namely the position of the leftmost zero. We prove, for q larger than a threshold $\bar{q} < 1$, a law of large number…

Fredrickson Andersen 模型与非顺从图上的噪声多数投票过程

Fredrickson Andersen Model and Noisy Majority Vote Process on Nonamenable Graphs

本文研究了非顺从图上的 Fredrickson-Andersen j-spin facilitated 模型与噪声多数投票过程，证明了前者的指数收敛性及后者的多重平衡测度存在性，并基于 decorated set systems 框架确立了零点时空簇直径的指数衰减尾部。

二维Fredrickson–Andersen模型

Fredrickson--Andersen model in two dimensions

本文综述二维Fredrickson–Andersen动力学约束自旋模型的最新数学进展，该模型是用于通过动力学约束重现过冷液体玻璃化现象的物理玩具模型。

Fredrickson-Andersen one spin facilitated model out of equilibrium

We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability $p\in[0,1]$ or $q=1-p$ respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution $ν$ different from the stationary product $p$-Bernoulli measure $μ$. We assume that, under $ν$, the mean distance between two nearest empty sites is uniformly bounded. We then prove conve…