Free fermionic probability theory and K-theoretic Schubert calculus

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Iwao, Shinsuke, Motegi, Kohei, Scrimshaw, Travis
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911372854427648
author Iwao, Shinsuke
Motegi, Kohei
Scrimshaw, Travis
author_facet Iwao, Shinsuke
Motegi, Kohei
Scrimshaw, Travis
contents For each of the four particle processes given by Dieker and Warren [arXiv:0707.1843], we show the $n$-step transition kernels are given by the (dual) (weak) refined symmetric Grothendieck functions up to a simple overall factor. We do so by encoding the particle dynamics as the basis of free fermions first introduced by the first author, which we translate into deformed Schur operators acting on partitions. We provide a direct combinatorial proof of this relationship in each case, where the defining tableaux naturally describe the particle motions.
format Preprint
id arxiv_https___arxiv_org_abs_2311_01116
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Free fermionic probability theory and K-theoretic Schubert calculus
Iwao, Shinsuke
Motegi, Kohei
Scrimshaw, Travis
Combinatorics
Mathematical Physics
Probability
05E05, 60K35, 14M15, 82B23, 05A19, 60B20
For each of the four particle processes given by Dieker and Warren [arXiv:0707.1843], we show the $n$-step transition kernels are given by the (dual) (weak) refined symmetric Grothendieck functions up to a simple overall factor. We do so by encoding the particle dynamics as the basis of free fermions first introduced by the first author, which we translate into deformed Schur operators acting on partitions. We provide a direct combinatorial proof of this relationship in each case, where the defining tableaux naturally describe the particle motions.
title Free fermionic probability theory and K-theoretic Schubert calculus
topic Combinatorics
Mathematical Physics
Probability
05E05, 60K35, 14M15, 82B23, 05A19, 60B20
url https://arxiv.org/abs/2311.01116