Universität Augsburg

Professor Dr. Elia Bisi
Technische Universität Wien
spricht am
Freitag, 21. Juli 2023
um
14:30 Uhr
im
Raum 2004 (L1)
über das Thema:
Abstract: 
The KPZ fixed point is conjectured to be the universal spacetime scaling limit of the models belonging to the KPZ universality class and it was rigorously constructed by Matetski, Quastel and Remenik (Acta Math., 2021) as a scaling limit of TASEP (Totally Asymmetric Simple Exclusion Process) with arbitrary initial configuration. We set up a new, alternative approach to the KPZ fixed point, based on combinatorial structures and nonintersecting path constructions, which also allows studying inhomogeneous interacting particle systems. More specifically, we consider a discretetime TASEP, where each particle jumps according to Bernoulli random variables with particledependent and timeinhomogeneous parameters, starting from an arbitrary initial configuration. We provide an explicit, stepbystep route from the very definition of the model to a Fredholm determinant representation of the joint distribution of the particle positions in terms of certain random walk hitting probabilities. Our tools include the combinatorics of the RobinsonSchenstedKnuth correspondence, intertwining relations, nonintersecting lattice paths, and determinantal point processes. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Markus Heydenreich 