Interacting Particle Systems and Jacobi Style Identities

Márton Balázs, Jessica Jay

Research output: Working paper

1 Downloads (Pure)

Abstract

We consider the family of nearest neighbour interacting particle systems on $\mathbb{Z}$ allowing $0$, $1$ or $2$ particles at a site. We parametrize a wide subfamily of processes exhibiting product blocking measure and show how this family can be "stood up" in the sense of Bal\'azs and Bowen (2018). By comparing measures we prove new three variable Jacobi style identities, related to counting certain generalised Frobenius partitions with a $2$-repetition condition. By specialising to specific processes we produce two variable identities that are shown to relate to Jacobi triple product and various other identities of combinatorial significance. The family of $k$-exclusion processes for arbitrary $k$ are also considered and are shown to give similar Jacobi style identities relating to counting generalised Frobenius partitions with a $k$-repetition condition.
Original languageEnglish
Place of PublicationResearch in the Mathematical Sciences
PublisherSpringer Nature
Number of pages39
Volume9
ISBN (Electronic)2197-9847
ISBN (Print)2522-0144
DOIs
Publication statusPublished - 10 Nov 2020
Externally publishedYes

Publication series

NameResearch in the Mathematical Sciences
PublisherSpringer Nature
No.3
Volume9
ISSN (Print)2522-0144
ISSN (Electronic)2197-9847

Keywords

  • math.PR
  • math.CO
  • math.NT
  • 60K35, 11P84, 05A19

Fingerprint

Dive into the research topics of 'Interacting Particle Systems and Jacobi Style Identities'. Together they form a unique fingerprint.

Cite this