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Seminários do IMPA

Probabilidade e Combinatória

Título
Ergodicity of the KPZ Fixed Point
Expositor
Leandro Pimentel

UFRJ
Data
Quarta-feira, 6 de setembro de 2017, 16:00
Local
Sala 347
Resumo

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik  arXiv:1701.00018, that describes the limit fluctuations of the height function associated to the totally asymmetric simple exclusion process (TASEP), and it is conjectured to be at the centre of the KPZ universality class. Our main result is that the KPZ incremental process converges weakly to its invariant measure, given by a two-sided Brownian motion with zero drift and diffusion coefficient 2 arXiv:1708.06006. The heart of the proof is the coupling method that allows us to compare the TASEP height function with its invariant process, which under the KPZ scaling turns into uniform estimates for the KPZ fixed point.