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

Abstract

AbstractWe 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.