Mixing times for constrained spin models


October 20, 2013


Fabio Martinelli


University of Roma 3


Consider the following Markov chain on the set of all possible zero-one labelings of a rooted binary tree of depth L: At each vertex v independently, a proposed new label (equally likely to be 0 or 1) is generated at rate 1. The proposed update is accepted iff either v is a leaf or both children of v are labeled “0”. A natural question is to determine the mixing time of this chain as a function of L. The above is just an example of a general class of chains in which the local update of a spin occurs only in the presence of a special (“facilitating”) configuration at neighboring vertices. Although the i.i.d. Bernoulli distribution remains a reversible stationary measure, the relaxation to equilibrium of these chains can be extremely complex, featuring dynamical phase transitions, metastability, dynamical heterogeneities and universal behavior. I will report on progress on the mixing times for these models.


Fabio Martinelli

Fabio Martinelli obtained his PhD in Physics in 1979, and is currently a Professor of Mathematics at the University of Roma 3. He is a recipient of a Marie-Curie Fellowship and was a visiting Miller Professor at UC Berkeley. He has also held visiting positions in UCLA and in Paris. Professor Martinelli is well known as the leading authority on the dynamics of the Ising model and related processes; his articles and surveys are the key references in the subject.