An Upper Tail Field of the KPZ Fixed Point
Statistics Seminars: Fall 2025
Department of Mathematical Sciences, IU Indianapolis
Organizer: Honglang Wang (hlwang at iu dot edu)
Talk time: 12:15-1:15pm (EST), 09/07/2025, Tuesday
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Title: An Upper Tail Field of the KPZ Fixed Point
Abstract: The KPZ fixed point is a (1+1)-dimensional space-time random field conjectured to be the universal limit for models within the Kardar-Parisi-Zhang (KPZ) universality class. We consider the KPZ fixed point with the narrow-wedge initial condition, conditioning on a large value at a specific point. By zooming in the neighborhood of this high point appropriately, we obtain a limiting random field which we call an upper tail field of the KPZ fixed point. Different from the KPZ fixed point, where the time parameter has to be nonnegative, the upper tail field is defined in the full 2-dimensional space. Particularly, if we zoom out the upper tail field appropriately, it behaves like a Brownian-type field in the negative time regime and the KPZ fixed point in the positive time regime. One main ingredient of the proof is an upper tail estimate of the joint tail probability functions of the KPZ fixed point near the given point, which generalizes the well-known one-point upper tail estimate of the GUE Tracy-Widom distribution. This is a joint work with Zhipeng Liu.
Bio: Dr. Ray Zhang is Postdoctoral Research Associate under the C.R. Wiley Instructorship in the Department of Mathematics, University of Utah. He obtained his Ph.D. in Mathematics from the University of Kansas in 2024. His research interests include primarily focuses on interacting particle systems, percolation models, and vertex models within the Kardar-Parisi-Zhang (KPZ) universality class, particularly their long-time asymptotic behaviours and large deviation phenomena. He is also interested in random matrix theory and related models from statistical mechanics.
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