Upper Tail Field of the KPZ Fixed Point in Probability Theory
Conditioning the KPZ fixed point on an extremely large height at a fixed space-time point and rescaling a shrinking neighborhood of that point yields a limiting random field, the upper tail field, defined over the whole two-dimensional space-time plane. This field interpolates between a Brownian-type field at negative times and the KPZ fixed point at positive times, capturing the transition between the two regimes seen before and after the conditioned high point. Its construction rests on a joint upper-tail estimate for the KPZ fixed point that generalizes the one-point upper-tail estimate of the GUE Tracy-Widom distribution.
An upper tail field of the KPZ fixed point Zhipeng Liu∗ Ruixuan Zhang† Abstract
The KPZ fixed point is a (1+1)-dimensional random space-time field, the conjectured universal scaling limit of interface-growth models in the Kardar-Parisi-Zhang universality class. This paper condit…