One-sided reflected Brownian motions and the KPZ fixed point

Abstract

We consider the system of one-sided reflected Brownian motions which 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.

Minor improvements. 15 pages

References in corpus (2)

• Fluctuation properties of the TASEP with periodic initial configuration
• Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition

Cited by in corpus (9)

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• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• KPZ fluctuations in finite volume
• Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
• Exact solution of interacting particle systems related to random matrices
• On the duality between particles and polymers