dc.contributor.author | Borodin, Alexei | |
dc.contributor.author | Corwin, Ivan | |
dc.contributor.author | Petrov, Leonid | |
dc.contributor.author | Sasamoto, Tomohiro | |
dc.date.accessioned | 2016-09-22T18:10:21Z | |
dc.date.available | 2016-09-22T18:10:21Z | |
dc.date.issued | 2015-07 | |
dc.date.submitted | 2015-01 | |
dc.identifier.issn | 0010-3616 | |
dc.identifier.issn | 1432-0916 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/104369 | |
dc.description.abstract | We develop spectral theory for the q-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result that implies completeness and biorthogonality statements for the Bethe ansatz eigenfunctions of the system. Owing to a Markov duality with the q-Hahn TASEP (a discrete-time generalization of TASEP with particles’ jump distribution being the orthogonality weight for the classical q-Hahn orthogonal polynomials), we write down moment formulas that characterize the fixed time distribution of the q-Hahn TASEP with general initial data. The Bethe ansatz eigenfunctions of the q-Hahn system degenerate into eigenfunctions of other (not necessarily stochastic) interacting particle systems solvable by the coordinate Bethe ansatz. This includes the ASEP, the (asymmetric) six-vertex model, and the Heisenberg XXZ spin chain (all models are on the infinite lattice). In this way, each of the latter systems possesses a spectral theory, too. In particular, biorthogonality of the ASEP eigenfunctions, which follows from the corresponding q-Hahn statement, implies symmetrization identities of Tracy and Widom (for ASEP with either step or step Bernoulli initial configuration) as corollaries. Another degeneration takes the q-Hahn system to the q-Boson particle system (dual to q-TASEP) studied in detail in our previous paper (2013). Thus, at the spectral theory level we unify two discrete-space regularizations of the Kardar–Parisi–Zhang equation/stochastic heat equation, namely, q-TASEP and ASEP. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.). (grant DMS-1056390) | en_US |
dc.publisher | Springer Berlin Heidelberg | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s00220-015-2424-7 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Springer Berlin Heidelberg | en_US |
dc.title | Spectral Theory for Interacting Particle Systems Solvable by Coordinate Bethe Ansatz | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Borodin, Alexei et al. “Spectral Theory for Interacting Particle Systems Solvable by Coordinate Bethe Ansatz.” Communications in Mathematical Physics 339.3 (2015): 1167–1245. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Borodin, Alexei | |
dc.relation.journal | Communications in Mathematical Physics | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2016-08-18T15:24:15Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer-Verlag Berlin Heidelberg | |
dspace.orderedauthors | Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro | en_US |
dspace.embargo.terms | N | en |
dc.identifier.orcid | https://orcid.org/0000-0002-2913-5238 | |
mit.license | OPEN_ACCESS_POLICY | en_US |