Zero-temperature Stochastic 2D Ising model and anisotropic curve-shortening flow

Add to your list(s) Download to your calendar using vCal

• Hubert Lacoin (Université Paris Dauphine )
• Tuesday 16 October 2012, 16:30-17:30
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact neb25.

The stochastic Ising model at zero temperature is the random evolution of a function {1,...,L}^{d \to {-,+}, the value of the function at one site is called spin. We start with the function that is uniformly equal to -1 on {1,...,L}}d and let spin configuration evolve according to the following rule: At each step choose a site at random and change it spin to give it either the spin of the majority of its neighbors or +/- with probability p / (1-p) if there are equally many + and – in its neighborhood. When doing so we consider that sites that are outside of the cube are counted among the neighbors if needed and that they have a fixed + spin. With this procedure, the cube will eventually be filled with + spins. How many step do you need to perform in average so that this happens? In our talk we will give an answer for this question in both symmetric case (p=1/2) and asymmetric case (p>1/2) and we are able to describe precisely the scaling limit of the set of $-$ spins when time and space are rescaled. For the symmetric case we relate this result to a conjecture called “Lifshitz Law”. The stochastic Ising model (or Glauber Dynamics for Ising model), is a rather simplified model introduced by theoretical Physicists to study dynamical properties of ferromagnet.

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator
• bld31

Note that ex-directory lists are not shown.