Title: Johansson's Conjecture is False on a Set of Times of Hausdorff Dimension 2/3
Speaker: Ivan Corwin
Speaker Info: Columbia University
Brief Description:
Special Note: Open to registered participants only (http://sites.math.northwestern.edu/mwp)
Abstract:
In 2002, Johansson conjectured that the maximum of the Airy2 process minus a parabola is almost surely achieved at a unique location. This result was proved a decade later by Corwin-Hammond using the Gibbs property of the Airy line ensemble, and later by different means by Moreno Flores-Quastel-Remenik, and Pimentel. Recently Pimentel extended this result to the fixed time spatial marginal of the KPZ fixed point with general initial data (Airy2 corresponds to narrow wedge initial data). None of these results rule out the possibility that at random times, the KPZ fixed point spatial marginal violated the maximizer uniqueness. In fact, we prove that with positive probability the set of such times is non-empty and in that case has Hausdorff dimension two-thirds. In terms of directed polymers, these are times when the endpoint of the zero-temperature polymer measure jumps from one location to another. This is joint work with Alan Hammond, Milind Hedge and Konstantin Matetski.Date: Friday, October 09, 2020