Fluctuations of particle systems determined by Schur generating functions
Name
1604.01110.pdf
Description
Submitted version
Size
1.17 MB
Format
Adobe PDF
Checksum (MD5)
a8070211c8e32ab684bc70357673131a
Author(s)
Bufetov, Alexey
Gorin, Vadim
Date Issued
November 2018
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Bufetov, Alexey, and Vadim Gorin. “Fluctuations of Particle Systems Determined by Schur Generating Functions.” Advances in Mathematics 338, 7 (November 2018): 702–81.
Version
Original manuscript
Abstract
We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a Central Limit Theorem (CLT) for such a configuration given certain conditions on the Schur generating function. As applications of this approach, we prove CLT's for several probabilistic models coming from asymptotic representation theory and statistical physics, including random lozenge and domino tilings, non-intersecting random walks, decompositions of tensor products of representations of unitary groups. Keywords: Schur functions; Asymptotic representation theory; Random tilings
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.AIM.2018.07.009
