Affiliation:
1. Department of Mathematics, University of Connecticut, Storrs, Mansfield, CT 06268, USA
Abstract
Abstract
We obtain a new formula to relate the value of a Schur polynomial with variables $(x_1,\ldots ,x_N)$ with values of Schur polynomials at $(1,\ldots ,1)$. This allows one to study the limit shape of perfect matchings on a square hexagon lattice with periodic weights and piecewise boundary conditions. In particular, when the edge weights satisfy certain conditions, asymptotics of the Schur function imply that the liquid region of the model in the scaling limit has multiple connected components, while the frozen boundary consists of disjoint cloud curves.
Funder
National Science Foundation
Simons Foundation
Publisher
Oxford University Press (OUP)
Reference35 articles.
1. Schur process and cylindrical partitions;Borodin;Duke Math. J.,2007
2. Schur dynamics of the Schur processes;Borodin;Adv. Math.,2011
3. Random tilings and Markov chains for interlacing particles;Borodin;Markov Process. Related Fields,2018
4. Dimers on rail yard graphs;Boutillier;Ann. Inst. Henri Poincaré D,2017
5. Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices;Boutillier
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