Independence property of the Busemann function in exactly solvable KPZ models
Abstract
The study of KadarParsiZhang (KPZ) universality class has been a subject of great interest among mathematicians and physicists over the past three decades. A notably successful approach for analyzing KPZ models is the coupling method, which hinges on understanding random growth from stationary initial conditions defined by Busemann functions. To advance in this direction, we investigate the independence property of the Busemann function across multiple directions in various exactly solvable KPZ models. These models encompass the corner growth model, the inversegamma polymer, Brownian lastpassage percolation, the O'ConnellYor polymer, the KPZ equation, and the directed landscape. In the context of the corner growth model, our result states that disjoint Busemann increments in different directions along a downright path are independent, as long as their associated semiinfinite geodesics have nonempty intersections almost surely. The proof for the independence utilizes the queueing representation of the Busemann process developed by Seppäläinen et al. As an application, our independence result yields a nearoptimal probability upper bound (missing by a logarithmic factor) for the rare event where the endpoint of a pointtoline inversegamma polymer is close to the diagonal.
 Publication:

arXiv eprints
 Pub Date:
 August 2023
 DOI:
 10.48550/arXiv.2308.11347
 arXiv:
 arXiv:2308.11347
 Bibcode:
 2023arXiv230811347S
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60K35;
 60K37
 EPrint:
 25 pages, 4 figures