Séminaire de Probabilités commun ICJ/UMPA

Distribution matches in stochastic vertex models and Macdonald processes

by Michael Wheeler

Amphi Schrödinger (ENS Lyon)

Amphi Schrödinger

ENS Lyon


(Séance commune avec le séminaire de physique théorique, de 13h30 à 14h30 en Amphi Schrödinger.)

One of the classic quantities in the six-vertex model is the domain wall partition function, which was computed as a determinant by Izergin. Most proofs of Izergin's formula are based on solving recursion relations and, as a consequence, a priori knowledge of the answer.

I will sketch a direct method for deriving Izergin's formula, based on Macdonald polynomials and their difference-operator eigenrelations (following ideas of Lascoux and Warnaar). The connection between the six-vertex model and Macdonald polynomials runs deeper still; I will discuss some intriguing distribution matches first observed by Borodin.