Interacting Particle Systems and Jacobi Style Identities

Márton Balázs, Jessica Jay

Allbwn ymchwil: Papur gweithio

1 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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.
Iaith wreiddiolSaesneg
Man cyhoeddiResearch in the Mathematical Sciences
CyhoeddwrSpringer Nature
Nifer y tudalennau39
Cyfrol9
ISBN (Electronig)2197-9847
ISBN (Argraffiad)2522-0144
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 10 Tach 2020
Cyhoeddwyd yn allanolIe

Cyfres gyhoeddiadau

EnwResearch in the Mathematical Sciences
CyhoeddwrSpringer Nature
Rhif3
Cyfrol9
ISSN (Argraffiad)2522-0144
ISSN (Electronig)2197-9847

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