Geodesic
The asymptotics of interlacing sequences and the growth of continual Young diagrams
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 13, Tome 205 (1993), pp. 21-29

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We obtain a series of concrete results establishing a somewhat unexpected connection between the asymptotic representation theory of symmetric groups and the classical results for one-dimensional problems of mathematical physics and function theory. In particular: 1) The universal character of the division of roots for a wide class of orthogonal polynomials is shown. 2) A connection between the Plancherel measure of the infinite symmetric group and Markov's moment problem is established. 3) Asymptotics of the Plancherel measure turns out to be connected with the soliton-like solution of the simplest quasilinear equation, $$ R'_t+RR'_x=0. $$ Bibliography: 14 titles. 
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     title = {The asymptotics of interlacing sequences and the growth of continual {Young} diagrams},
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S. Kerov. The asymptotics of interlacing sequences and the growth of continual Young diagrams. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 13, Tome 205 (1993), pp. 21-29. http://geodesic.mathdoc.fr/item/ZNSL_1993_205_a2/