SPMES: Planar percolation and the loop O(n) model скачать в хорошем качестве

SPMES: Planar percolation and the loop O(n) model

Seminário de Probabilidade e Mecânica Estatística Título: Planar percolation and the loop O(n) model Palestrante: Matan Harel, Northeastern University Playlist dos videos: https://bit.ly/30ZkHWe Resumo: Consider a tail trivial, positively associated site percolation process such that the set of open vertices is stochastically dominated by the set of closed ones. We show that, for any planar graph G, such a process must contain zero or infinitely many infinite connected components. The assumptions cover Bernoulli site percolation at parameter p less than or equal to one half, resolving a conjecture of Benjamini and Schramm. As a corollary, we prove that p_c is greater than or equal to 1/2 for any unimodular, invariantly amenable planar graphs. We will then apply this percolation statement to the loop O(n) model on the hexagonal lattice, and show that, whenever n is between 1 and 2 and x is between 1/sqrt(2) and 1, the model exhibits infinitely many loops surrounding every face of the lattice, giving strong evidence for conformally invariant behavior in the scaling limit (as conjectured by Nienhuis). 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: https://linktr.ee/impabr IMPA - Instituto de Matemática Pura e Aplicada © http://www.impa.br | http://impa.br/videos #spmes Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.