Jeffrey Kuan - Universality of dynamic processes using Drinfel'd twisters - IPAM at UCLA

Recorded 23 May 2024. Jeffrey Kuan of Texas A&M University - College Station presents "Universality of dynamic processes using Drinfel'd twisters" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop.
Abstract: The concept of 'universality' motivates a wide variety of probability and mathematical physics problems, going back to the classical central limit theorem. Most recently, the Kardar--Parisi--Zhang universality class has been proven to have Tracy--Widom fluctuations in the long-time asymptotics. In this talk, I will present a new universality result about the long-time asymptotics of so--called ``dynamic'' processes. The asymptotic fluctuations are related to the Tracy--Widom distribution. The proof will utilize a duality of Markov processes, which is constructed using Drinfel'd twisters of the quantum group U_q(sl_2), viewed as a quasi-triangular quasi-Hopf algebra. The orthogonality of the duality functions allow for an asymptotic analysis.
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