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CATEGORIES:Probability
SUMMARY:Zero-temperature Stochastic 2D Ising model and ani
sotropic curve-shortening flow - Hubert Lacoin (Un
iversité Paris Dauphine )
DTSTART;TZID=Europe/London:20121016T163000
DTEND;TZID=Europe/London:20121016T173000
UID:TALK40564AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40564
DESCRIPTION:The stochastic Ising model at zero temperature is
the random evolution of a\nfunction {1\,...\,L}^d
\\to {-\,+}\, the value of the function at one sit
e is\ncalled spin.\nWe start with the function tha
t is uniformly equal to -1 on {1\,...\,L}^d and\n
let spin configuration evolve according to the fol
lowing rule: At each step\nchoose a site at random
and change it spin to give it either the spin of
the\nmajority of its neighbors or +/- with probabi
lity p / (1-p) if there are\nequally many + and -
in its neighborhood. When doing so we consider tha
t\nsites that are outside of the cube are counted
among the neighbors if needed\nand that they have
a fixed + spin.\nWith this procedure\, the cube wi
ll eventually be filled with + spins.\nHow many st
ep do you need to perform in average so that this
happens?\nIn our talk we will give an answer for t
his question in both symmetric case\n(p=1/2) and a
symmetric case (p>1/2)\nand we are able to describ
e precisely the scaling limit of the set of $-$\ns
pins when time and space are rescaled.\nFor the sy
mmetric case we relate this result to a conjecture
called\n"Lifshitz Law". The stochastic Ising mode
l (or Glauber Dynamics for Ising\nmodel)\, is a ra
ther simplified model introduced by theoretical Ph
ysicists to\nstudy dynamical properties of ferroma
gnet.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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