The ASEP and Determinantal Point Processes
Name
1608.01564.pdf
Description
Submitted version
Size
650.03 KB
Format
Adobe PDF
Checksum (MD5)
3276a1b24faf4ce5fe7e9f9862129d41
Author(s)
Borodin, Alexei
Olshanski, Grigori
Date Issued
2017
Journal
Communications in Mathematical Physics
Publisher
Springer Nature
Version
Original manuscript
Abstract
© 2017, Springer-Verlag Berlin Heidelberg. We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi matrices. For classical weights, we show how such ensembles arise as limits of various hypergeometric orthogonal polynomial ensembles. We then prove that the q-Laplace transform of the height function of the ASEP with step initial condition is equal to the expectation of a simple multiplicative functional on a discrete Laguerre ensemble—a member of the new family. This allows us to obtain the large time asymptotics of the ASEP in three limit regimes: (a) for finitely many rightmost particles; (b) GUE Tracy–Widom asymptotics of the height function; (c) KPZ asymptotics of the height function for the ASEP with weak asymmetry. We also give similar results for two instances of the stochastic six vertex model in a quadrant. The proofs are based on limit transitions for the corresponding determinantal point processes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/S00220-017-2858-1
