SPMES: Strong disorder and very strong disorder are equivalent for directed polymers - Hubert Lacoin

Seminário de Probabilidade e Mecânica Estatística
Título: Strong disorder and very strong disorder are equivalent for directed polymers
Palestrante: Hubert Lacoin, IMPA
Playlist dos videos: bit.ly/30ZkHWe
Resumo: The Directed Polymer in a Random Environment is a statistical mechanics model, which has been introduced (in dimension 1) as a toy model to study the interfaces of the planar Ising model with random coupling constants. The model was shortly afterwards generalized to higher dimensions. In this latter case, rather than an effective interface model, the directed polymer in a random environment can be thought of as modeling the behavior of a stretched polymer in a solution with impurities. The interest in the model model, triggered by its rich phenomenology, has since then generated a plentiful literature in theoretical physics and mathematics. An important topic for the directed polymer is the so-called localization transition. This transition can be defined in terms of the asymptotic behavior of the renormalized partition function of the model. If the finite volume partition function converges to an almost surely positive limit we say that weak disorder holds. On the other hand, if it converges to zero almost surely, we say that strong disorder holds. It has been proved that weak disorder implies that the distribution of the rescaled polymer converges to standard Brownian motion while some localization results have been proved under the strong disorder assumptions. Much stronger characterizations of disorder-induced localization have been obtained under the stronger assumption that the partition function converges to zero exponentially fast. This latter regime is known as the very strong disorder regime. It has long been conjectured that strong and very strong disorder are equivalent. In this talk we will sketch a proof of this conjecture.
Joint with Stefan Junk, Gakushuin University
Apoio:
IMPA
Instituto Superior Técnico de Lisboa
UFBA
UFMG
UFRGS
UFRJ
Unicamp
Universidade do Porto
USP
Comitê científico:
Luiz Renato Fontes (USP)
Tertuliano Franco (UFBA)
Nancy Lopes Garcia (Unicamp)
Patrícia Gonçalves (IST, Lisboa)
Marcelo Hilário (UFMG)
Roberto Imbuzeiro (Coordenador, IMPA)
Claudio Landim (Coordenador, IMPA)
Adriana Neumann (UFRGS)
Serguei Popov (UP, Porto)
Glauco Valle (UFRJ)
Redes Sociais do IMPA: linktr.ee/impabr
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