Random particle systems and Schur processes

• Ano de defesa: 2023
• Autor(a) principal: Vendruscollo, Victor Guerreiro
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Análise assintótica; Asymptotic analysis; Funções simétricas; Integrable probability; Probabilidade integrável; Processos de Schur; Schur processes; Symmetric functions; TASEP
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062023-110944/

It may sound absurd to believe that a traffic jam model, eigenvalues of random matrices, and the length of the longest increasing subsequence of random permutations have a connection. Mathematicians say otherwise. Surprising results show that some fluctuations of these and many other models have the same asymptotic behavior. The development of integrable probability, a branch of representation theory applied to probability, is crucial for such findings. The totally asymmetric simple exclusion process (TASEP) is an interacting particle system that simulates traffic. We find the TASEP in a particular parametrization of a more general object, the Schur process, which is the main object of this study.