Nearest neighbor Markov dynamics on Macdonald processes
Name
Borodin_Nearest neighbor Markov.pdf
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1.29 MB
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Adobe PDF
Checksum (MD5)
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Author(s)
Borodin, Alexei
Petrov, Leonid
Date Issued
April 2016
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Borodin, Alexei and Leonid Petrov. “Nearest Neighbor Markov Dynamics on Macdonald Processes.” Advances in Mathematics 300 (September 2016): 71–155 © 2016 Elsevier
Version
Original manuscript
Abstract
Macdonald processes are certain probability measures on two-dimensional arrays of interlacing particles introduced by Borodin and Corwin in [7]. They are defined in terms of nonnegative specializations of the Macdonald symmetric functions and depend on two parameters q,t∈[0;1). Our main result is a classification of continuous time, nearest neighbor Markov dynamics on the space of interlacing arrays that act nicely on Macdonald processes. The classification unites known examples of such dynamics and also yields many new ones. When t=0, one dynamics leads to a new integrable interacting particle system on the one-dimensional lattice, which is a q-deformation of the PushTASEP (= long-range TASEP). When q=t, the Macdonald processes become the Schur processes of Okounkov and Reshetikhin [41]. In this degeneration, we discover new Robinson–Schensted-type correspondences between words and pairs of Young tableaux that govern some of our dynamics. Keywords: Macdonald processes; q-Whittaker processes; TASEP; q-TASEP; Kardar–Parisi–Zhang universality class; Interlacing particle arrays; Gelfand–Tsetlin schemes; Multivariate Markov dynamics; Young diagrams; Young tableaux; Robinson–Schensted–Knuth correspondence; Randomized Robinson–Schensted correspondence
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.AIM.2016.03.016
