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Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings
- Part of
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- Journal:
- Combinatorics, Probability and Computing / Volume 31 / Issue 4 / July 2022
- Published online by Cambridge University Press:
- 18 October 2021, pp. 550-573
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- Article
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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.
