Seminário de Probabilidade e Análise Estocástica  RSS

09/03/2022, 16:00 — 17:00 — Sala P3.10, Pavilhão de Matemática Online
, UC Berkeley

Markovian solutions for scalar conservation laws

Groeneboom in 1989 discovered an explicit formula for the law of the entropy solution to Burgers' equation when the initial condition is a white noise. The method of his proof relied extensively on probabilistic methods and in particular on the sophisticated excursion theory for diffusions. Recently, by verifying a conjecture of Menon and Srinivasan, Kaspar and Rezakhanlou managed to prove a closure theorem for Markovian solutions to scalar conservation laws which bridged the probabilistic problem to kinetic theory. In this talk, I present a new and significantly shorter proof of Groeneboom's results. This approach builds on these recent developments, and a central limit theorem for certain Markovian jump processes. I also discuss how a kinetic theory can be developed when we add an external force to the Burgers' equation.


Excepto para as sessões mais antigas trata-se de sessões do Seminário de Probabilidade e Mecânica Estatística do IMPA e co-organizado com outras instituições, em particular o Instituto Superior Técnico.