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SUMMARY:Bootstrap percolation and kinetically constrained spin models: cri
 tical lengths and mixing time scales - Fabio Martinelli (Università degli
  Studi Roma Tre)
DTSTART:20160713T084500Z
DTEND:20160713T093000Z
UID:TALK66730@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Cristina Toninelli (Univ Paris VII  Diderot)
 \, Rob Morris (IMPA) <br></span> <span><br>In recent years\, a great deal 
 of progress has been made in understanding the  behaviour of a particular 
 class of monotone cellular automata\, commonly known as  bootstrap percola
 tion. In particular\, if one considers only two-dimensional  automata\, th
 en we now have a fairly precise understanding of the typical  evolution of
  these processes\, starting from p-random initial conditions of  infected 
 sites. Given a bootstrap model\, one can consider the associated  kinetica
 lly constrained spin model in which the state (infected or healthy) of a  
 vertex is resampled (independently) at rate 1 by tossing a p-coin if it co
 uld be  infected in the next step by the bootstrap process\, and remains i
 n its current  state otherwise. Here p is the probability of infection. Th
 e main interest in  KCM&rsquo\;s stems from the fact that\, as p &rarr\; 0
 \, they mimic some of the most striking  features of the glass transition\
 , a major and still largely open problem in  condensed matter physics. In 
 this talk\, motivated by recent universality results  for bootstrap percol
 ation\, I&rsquo\;ll discuss some &ldquo\;universality conjectures&rdquo\; 
  concerning the growth of the (random) infection time of the origin in a K
 CM as p  &rarr\; 0. Joint project with R. Morris (IMPA) and C. Toninelli (
 Paris VII)\,</span>
LOCATION:Seminar Room 1\, Newton Institute
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