The limit shape in the double-elliptic generalization of the Vershik-Kerov problem is governed by a genus two algebraic curve.
Z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and beta=2 random matrix ensembles
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abstract
We suggest an hierarchy of all the results known so far about the connection of the asymptotics of combinatorial or representation theoretic problems with ``beta=2 ensembles'' arising in the random matrix theory. We show that all such results are, essentially, degenerations of one general situation arising from so-called generalized regular representations of the infinite symmetric group.
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Vershik-Kerov in higher times
The limit shape in the double-elliptic generalization of the Vershik-Kerov problem is governed by a genus two algebraic curve.