Quantum cohomology of Grassmannian and unitary Dyson Brownian motion - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... (Preprint) Year : 2022

Quantum cohomology of Grassmannian and unitary Dyson Brownian motion

Cohomologie quantique des Grassmanniennes et mouvement Brownien de Dyson unitaire

Jérémie Guilhot

Abstract

We study a class of commuting Markov kernels whose simplest element describes the movement of k particles on a discrete circle of size n conditioned to not intersect each other. Such Markov kernels are related to the quantum cohomology ring of Grassmannian, which is an algebraic object counting analytic maps from P 1 (C) to the Grassmannian space of k-dimensional vector subspaces of C n with prescribed constraints at some points of P 1 (C). We obtain a Berry-Esseen theorem and a local limit theorem for an arbitrary product of approximately n 2 Markov kernels belonging to the above class, when k is fixed. As a byproduct of those results, we derive asymptotic formulas for the quantum cohomology ring of the Grassmannian in terms of the heat kernel on SU (k). To Philippe Biane, for his 60th birthday.
Fichier principal
Vignette du fichier
qcohomology_dyson.pdf (655.56 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03868620 , version 1 (23-11-2022)

Identifiers

  • HAL Id : hal-03868620 , version 1

Cite

Jérémie Guilhot, Cédric Lecouvey, Pierre Tarrago. Quantum cohomology of Grassmannian and unitary Dyson Brownian motion. 2022. ⟨hal-03868620⟩
38 View
16 Download

Share

Gmail Mastodon Facebook X LinkedIn More