The paper proves new asymptotic expansion formulas for Harish-Chandra and Schur generating functions, links them to (quantized) infinitesimal freeness, and demonstrates a BBP-type phase transition in domino tilings.
Biane, Approximate factorization and concentration for characters of symmetric groups, International Mathematics Research Notices, 2001, no.\ 4, (2001), 179--192
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Asymptotics of Harish-Chandra transform and infinitesimal freeness
The paper proves new asymptotic expansion formulas for Harish-Chandra and Schur generating functions, links them to (quantized) infinitesimal freeness, and demonstrates a BBP-type phase transition in domino tilings.