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• W2964014123 abstract "We study a kinetically constrained Ising process (KCIP) associated with a graph $G$ and density parameter $p$; this process is an interacting particle system with state space ${0,1}^{G}$, the location of the particles. The number of particles at stationarity follows the $operatorname{Binomial}(|G|,p$) distribution, conditioned on having at least one particle. The “constraint” in the name of the process refers to the rule that a vertex cannot change its state unless it has at least one neighbour in state “1”. The KCIP has been proposed by statistical physicists as a model for the glass transition, and more recently as a simple algorithm for data storage in computer networks. In this note, we study the mixing time of this process on the torus $G=mathbb{Z}_{L}^{d}$, $dgeq3$, in the low-density regime $p=frac{c}{|G|}$ for arbitrary $0<c<infty$; this regime is the subject of a conjecture of Aldous and is natural in the context of computer networks. Our results provide a counterexample to Aldous’ conjecture, suggest a natural modification of the conjecture, and show that this modification is correct up to logarithmic factors. The methods developed in this paper also provide a strategy for tackling Aldous’ conjecture for other graphs." @default.
• W2964014123 created "2019-07-30" @default.
• W2964014123 creator A5051955613 @default.
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• W2964014123 date "2017-03-01" @default.
• W2964014123 modified "2023-09-28" @default.
• W2964014123 title "Mixing times for a constrained Ising process on the torus at low density" @default.
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• W2964014123 doi "https://doi.org/10.1214/15-aop1080" @default.
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