English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the coarsening model (zero-temperature Ising Glauber dynamics) on$\mathbb{Z}^d$ (for $d \geq 2$) with an asymmetric tie-breaking rule. This is aMarkov process on the state space $\{-1,+1\}^{\mathbb{Z}^d}$ of "spinconfigurations" in which each vertex updates its spin to agree with a majorityof its neighbors at the arrival times of a Poisson process. If a vertex hasequally many $+1$ and $-1$ neighbors, then it updates its spin value to $+1$with probability $q \in [0,1]$ and to $-1$ with probability $1-q$. The initialstate of this Markov chain is distributed according to a product measure withprobability $p$ for a spin to be $+1$. In this paper, we show that for anygiven $p>0$, there exist $q$ close enough to 1 such that a.s. every spin has alimit of $+1$. This is of particular interest for small values of $p$, forwhich it is known that if $q=1/2$, a.s. all spins have a limit of $-1$. Fordimension $d=2$, we also obtain near-exponential convergence rates for $q$sufficiently large, and for general $d$, we obtain stretched exponential ratesindependent of $d$. Two important ingredients in our proofs are refinements ofblock arguments of Fontes-Schonmann-Sidoravicius and a novel exponential largedeviation bound for the Asymmetric Simple Exclusion Process.

Coarsening model on $\mathbb{Z}^d$ with biased zero-energy flips and an exponential large deviation bound for ASEP