Séminaire de Probabilités commun ICJ/UMPA

Distribution matches in stochastic vertex models and Macdonald processes

by Michael Wheeler

Europe/Paris
Amphi Schrödinger (ENS Lyon)

Amphi Schrödinger

ENS Lyon

Description

(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.

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