Journal article
Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process
G Barraquand, A Borodin, I Corwin, M Wheeler
Duke Mathematical Journal | DUKE UNIV PRESS | Published : 2018
Abstract
We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition.We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin fluctuates asymptotically (in large time τ) according to the Tracy-Widom Gaussian orthogonal ensemble distribution on the τ1/3-scale. This is the first example of Kardar-Parisi-Zhang asymptotics for a half-space system outside the class of free-fermionic/determinantal/ Pfaffian models. Our main tool in this analysis is a new class of probability measures on Young diagrams that we call half-space Macdonald processes, as well as two surprising relations. The fir..
View full abstractRelated Projects (1)
Grants
Awarded by Radcliffe Institute for Advanced Study, Harvard University
Funding Acknowledgements
Borodin's work was partially supported by National Science Foundation (NSF) grant DMS-1607901 and by fellowships from the Radcliffe Institute for Advanced Study and the Simons Foundation. Corwin's work was partially supported by the NSF through grant DMS-1208998, the Clay Mathematics Institute through a Clay Research Fellowship, the Poincare Institute through the Poincare Chair, and the Packard Foundation through a Packard Fellowship for Science and Engineering. Barraquand's work was partially supported by the Packard Foundation through Corwin's fellowship. Wheeler's work was partially supported by Australian Research Council grant DE160100958.