# Discrete Markov Chains: mixing times and beyond

Programa Temático – Teoria da Probabilidade e Mecânica Estatística Rigorosa

IMPA, Rio de Janeiro, from 10/27 to 10/31, 2014

## Special minicourse: Oct 20 – 24,2014

 Tuesday, 21 Thursday, 23 Friday, 24 Alexandre Stauffer (Bath) Intermediate Markov Chain Theory 2:00PM – 4:30PM

The analysis of discrete Markov chains has been a fruitful research topic for more than thirty years. Questions related to Markov chain mixing times have been especially prominent, both due to their relation to Markov Chain Monte Carlo algorithms (MCMC) and their various connections to other areas of Mathematics such as Analysis, Representation Theory and rigorous Statistical Mechanics.

Recent years have witnessed progress in mixing times as well as many important results that go beyond mixing. This workshop will cover the state of the art in these topics, giving participants ample time for discussions and collaboration.

In order to facilitate student involvemet, a special one-week minicourse, on intermediate Markov chain theory, will be offered by Alexandre Stauffer (Bath) in the week preceeding the workshop.

Participants

## Invited Speakers

David Belius (CRM Montréal)
The subleading order of 2d cover times

Nathanaël Berestycki (University of Cambridge)
Cutoff for conjugacy-invariant random walks on permutation group

Hubert Lacoin (CNRS/IMPA)
A product chain without cutoff

Eyal Lubetzky (New York University)
Random walk on the random graph

Fabio Martinelli (Roma Tre)
Relaxation time of East models in d-dimensions

Yuval Peres (One Microsoft Way)
Characterization of cutoff for reversible Markov chains

Allan Sly (Berkeley)
Effect of initial conditions in the high temperature Ising Model

Aaron Smith (Stanford)
Mixing time of the constrained Ising process on the lattice at low density

Alexandre Stauffer (Bath)
Random lattice triangulations

## Minicourse

Johel Beltrán (PUC Perú)
A martingale approach to metastability

## Organizers

Milton Jara (IMPA)
Roberto Imbuzeiro Oliveira (IMPA)
Yuval Peres (Microsoft Research)

Picture

## Poster Session

#### Poster Session

A martingale approach to waiting time problems in Markov chains
Renato Gava (Universidade Federal de São Carlos)

Poster Session Submission:

To submit a communication, the participant needs to prepare an abstract in LaTeX using the standard format of the workshop which can be downloaded by clicking here.

The text must be processed directly from LaTex to the .PDF format. The .PDF and .tex files should be sent to the e-mail eventos@impa.br not later than September 19, 2014.

## Registration

Prices for Registration

 Category Prices Professors (Ph.D´s) R$120,00 Students (Master and Ph.D) R$ 60,00 IMPA’s Students R\$ 40,00

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