One-sided reflected Brownian motions and the KPZ fixed point
Author
dc.contributor.author
Nica, Mihai
Author
dc.contributor.author
Quastel, Jeremy
Author
dc.contributor.author
Remenik Zisis, Daniel
Admission date
dc.date.accessioned
2021-05-27T23:17:48Z
Available date
dc.date.available
2021-05-27T23:17:48Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Forum of Mathematics Sigma (2020), 8:e63, 1–16
es_ES
Identifier
dc.identifier.other
10.1017/fms.2020.56
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/179859
Abstract
dc.description.abstract
We consider the system of one-sided reflected Brownian motions that is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling-invariant Markov process defined in [MQR17] and believed to govern the long-time, large-scale fluctuations for all models in the KPZ universality class. Brownian last-passage percolation was shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.
es_ES
Patrocinador
dc.description.sponsorship
Natural Sciences and Engineering Research Council of Canada (NSERC)
CGIAR
Conicyt Basal-CMM Proyecto/Grant
PAI AFB-170001
Programa Iniciativa Cientifica Milenio grant through Nucleus Millenium Stochastic Models of Complex and Disordered Systems
NC120062
Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)
CONICYT FONDECYT
120194