DH 3rd floor SR

Sequential Monte Carlo Samplers are a class of stochastic algorithms for

Monte Carlo integral estimation w.r.t. probability distributions, which combine

elements of Markov chain Monte Carlo methods and importance sampling/resampling

schemes. We develop a stability analysis by functional inequalities for a

nonlinear flow of probability measures describing the limit behaviour of the

methods as the number of particles tends to infinity. Stability results are

derived both under global and local assumptions on the generator of the

underlying Metropolis dynamics. This allows us to prove that the combined

methods sometimes have good asymptotic stability properties in multimodal setups

where traditional MCMC methods mix extremely slowly. For example, this holds for

the mean field Ising model at all temperatures.

 

  We present a link between polymer pinning by a columnar defect in a random medium and a particular model of interacting particles on the line, related to polynuclear growth. While the question of whether an arbitrarily small intensity for the defect always results in pinning is still open, in a 'randomized' version of the model, which is closely related to the zero-temperature Glauber dynamics of the Ising model, we are able to obtain explicit results and a complete understanding of the process. This is joint work with Vladas Sidoravicius and Maria Eulalia Vares.  

 

We will see how Dynkin's isomorphism emerges from the "loop soup" introduced by

Lawler and Werner.

We report on two joint works with Jeremy Quastel and Alejandro Ramirez, on an

interacting particle system which can be viewed as a combustion mechanism or a

chemical reaction.

We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in

which $Y$ particles do not move while $X$ particles move as independent

continuous time, simple symmetric random walks. $Y$ particles are transformed

instantaneously to $X$ particles upon contact.

We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the

right of the origin, and define a class of configurations of the $X$ particles

to the left of the origin having a finite $l^1$ norm with a specified

exponential weight. Starting from any configuration of $X$ particles to the left

of the origin within such a class, we prove a central limit theorem for the

position of the rightmost visited site of the $X$ particles.