Universality of dynamic processes using Drinfel'd twisters

Jeffrey Kuan
Texas A&M University - College Station

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.

Presentation (PDF File)

Back to Workshop IV: Vertex Models: Algebraic and Probabilistic Aspects of Universality