Symmetric elliptic functions, IRF models, and dynamic exclusion processes
Name
1701.05239.pdf
Description
Submitted version
Size
1.5 MB
Format
Adobe PDF
Checksum (MD5)
4b2382c5bab02ba111f3218629cc600c
Author(s)
Borodin, Alexei
Date Issued
2020
Journal
Journal of the European Mathematical Society
Publisher
European Mathematical Society Publishing House
Version
Original manuscript
Abstract
© European Mathematical Society 2020 We introduce stochastic Interaction-Round-a-Face (IRF) models that are related to representations of the elliptic quantum group Eτ,η(sl2). For stochastic IRF models in a quadrant, we evaluate averages for a broad family of observables that can be viewed as higher analogs of q-moments of the height function for the stochastic (higher spin) six vertex models. In a certain limit, the stochastic IRF models degenerate to (1+1)d interacting particle systems that we call dynamic ASEP and SSEP; their jump rates depend on local values of the height function. For the step initial condition, we evaluate averages of observables for them as well, and use those to investigate one-point asymptotics of the dynamic SSEP. The construction and proofs are based on remarkable properties (branching and Pieri rules, Cauchy identities) of a (seemingly new) family of symmetric elliptic functions that arise as matrix elements in an infinite volume limit of the algebraic Bethe ansatz for Eτ,η(sl2).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4171/JEMS/947
