Seminario di  Probabilita' a Roma Tre

Niccolo' Torri
(Universite' Lyon 1)

Titolo: A stretched-exponential Pinning Model with heavy-tailed
Disorder

Mercoledi' 08 Ottobre 2014 ORE 14:30

Dipartimento di Matematica e Fisica
Universita' degli Studi Roma Tre
AULA 311 (SEMINARI) Largo San L. Murialdo,1

Abstract:
We study the so-called pinning model, which describes the behavior of
a Markov chain interacting with a distinguished state. The interaction
depends on an external source of randomness, called disorder, which
can attract or repel the Markov chain path. We focus on the case when
the disorder is heavy-tailed, with infinite mean, while the return
times of the Markov chain have a stretched-exponential distribution.
We prove that the set of times at which the Markov chain visits the
distinguished state, suitably rescaled, converges in distribution to a
limit set, which depends only on the disorder and on the interplay of
the parameters. We also show that there exists a random threshold of
the interaction strength, below which the limit set is trivial. As a
byproduct of our techniques, we improve and complete a result of
Auffinger and Louidor on the directed polymer in a random environment
with heavy tailed disorder.