Título: Probability Webinar - Integration by Parts and the KPZ Two-Point Function
Palestrante: Leandro P. R. Pimentel (IM-UFRJ)
Data: 28 de setembro
Local: Transmissão online
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Resumo: All models in the 1+1 Kardar-Parisi-Zhang (KPZ) universality class have fluctuations that converge under KPZ scaling to a universal Markov process, named the KPZ fixed point. In this talk we consider this universal process starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to establish a key relation between the two-point (correlation) function and the location of the maximum of an Airy process plus a Brownian motion with a negative parabolic drift. Integration by parts also allows us to deduce the density of this location in terms of the second derivative of the variance of the KPZ fixed point. We further develop an adaptation of Malliavin-Stein method that implies asymptotic independence with respect to the initial data.