One-sided reflected Brownian motions and the KPZ fixed point
Artículo

Open/ Download
Access note
Acceso Abierto
Publication date
2020
Author
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.
Patrocinador
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
Indexation
Artículo de publicación ISI Artículo de publicación SCOPUS
Quote Item
Forum of Mathematics Sigma (2020), 8:e63, 1–16
Collections
The following license files are associated with this item: