Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings-Reference-Cited by-同舟云学术

Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

Published:2021-10-18 Issue: Volume: Page:1-24
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

Morales Alejandro H.,Pak Igor,Tassy Martin

Abstract

Abstract We prove and generalise a conjecture in [MPP4] about the asymptotics of

$\frac{1}{\sqrt{n!}} f^{\lambda/\mu}$

, where

$f^{\lambda/\mu}$

is the number of standard Young tableaux of skew shape

$\lambda/\mu$

which have stable limit shape under the

$1/\sqrt{n}$

scaling. The proof is based on the variational principle on the partition function of certain weighted lozenge tilings.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference35 articles.

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4. Limit shapes for random square Young tableaux

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