Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 2923
Articles: 1'999'196
Articles rated: 2574

01 October 2020
 
  » arxiv » 1910.6782

 Article overview


Universality for critical KCM: finite number of stable directions
Ivailo Hartarsky ; Fabio Martinelli ; Cristina Toninelli ;
Date 15 Oct 2019
AbstractIn this paper we consider kinetically constrained models (KCM) on $mathbb Z^2$ with general update families $mathcal U$. For $mathcal U$ belonging to the so-called ’’critical class’’ our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper Mar^ech’e and two of the present authors proved that if $mathcal U$ has an infinite number of ’’stable directions’’, then on a doubly logarithmic scale the above divergence is twice the one in the corresponding $mathcal U$-bootstrap percolation.
Here we prove instead that, contrary to previous conjectures, in the complementary case the two divergences are the same. In particular, we establish the full universality partition for critical $mathcal U$. The main novel contribution is the identification of the leading mechanism governing the motion of infected critical droplets. It consists of a peculiar hierarchical combination of mesoscopic East-like motions. Even if each path separately depends on the details of $mathcal U$, their combination gives rise to an essentially isotropic motion of the infected critical droplets. In particular, the only surviving information about the detailed structure of $mathcal U$ is its difficulty. On a technical level the above mechanism is implemented through a sequence of Poincar’e inequalities yielding the correct scaling of the infection time.
Source arXiv, 1910.6782
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (https://commoncrawl.org/faq/)






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica