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SUMMARY:Zero-temperature Stochastic 2D Ising model and anisotropic curve-s
 hortening flow - Hubert Lacoin (Université Paris Dauphine )
DTSTART:20121016T153000Z
DTEND:20121016T163000Z
UID:TALK40564@talks.cam.ac.uk
CONTACT:12974
DESCRIPTION:The stochastic Ising model at zero temperature is the random e
 volution of a\nfunction {1\,...\,L}^d \\to {-\,+}\, the value of the funct
 ion at one site is\ncalled spin.\nWe start with the function that is unifo
 rmly equal to -1 on {1\,...\,L}^d  and\nlet spin configuration evolve acco
 rding to the following rule: At each step\nchoose a site at random and cha
 nge it spin to give it either the spin of the\nmajority of its neighbors o
 r +/- with probability p / (1-p) if there are\nequally many + and - in its
  neighborhood. When doing so we consider that\nsites that are outside of t
 he cube are counted among the neighbors if needed\nand that they have a fi
 xed + spin.\nWith this procedure\, the cube will eventually be filled with
  + spins.\nHow many step do you need to perform in average so that this ha
 ppens?\nIn our talk we will give an answer for this question in both symme
 tric case\n(p=1/2) and asymmetric case (p>1/2)\nand we are able to describ
 e precisely the scaling limit of the set of $-$\nspins when time and space
  are rescaled.\nFor the symmetric case we relate this result to a conjectu
 re called\n"Lifshitz Law". The stochastic Ising model (or Glauber Dynamics
  for Ising\nmodel)\, is a rather simplified model introduced by theoretica
 l Physicists to\nstudy dynamical properties of ferromagnet.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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