Seminario Análisis y Aplicaciones
Probabilistic limit shapes and harmonic envelopes
Ponente: Istvan Prause (Abo Akademi University)Fecha: miércoles 16 de octubre de 2024 - 12:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
Limit shapes are deterministic surfaces in \(\mathbb{R}^3\) which arise in the macroscopic limit of discrete random surfaces associated to various probability models such as domino tilings, random Young tableaux or vertex models. The limit surface is a minimiser of a variational problem with a surface tension which encodes the local entropy of the model. I’ll present a geometric ”harmonic envelope method” which applies to a variety of models. I’ll illustrate the method in detail by considering random Young tableaux on an arbitrary diagram and related problems. The talk is based in part on joint work with Rick Kenyon.
