Stochastic Monotonicity in Young Graph and Thoma Theorem
Author(s)Bufetov, Alexey; Gorin, Vadim
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We show that the order on probability measures, inherited from the dominance order on the Young diagrams, is preserved under natural maps reducing the number of boxes in a diagram by 1. As a corollary, we give a new proof of the Thoma theorem on the structure of characters of the infinite symmetric group. We present several conjectures generalizing our result. One of them (if it is true) would imply the Kerov's conjecture on the classification of all homomorphisms from the algebra of symmetric functions into R, which are non-negative on Hall-Littlewood polynomials.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
International Mathematics Research Notices
Oxford University Press (OUP)
Bufetov, Alexey and Vadim Gorin. “Stochastic Monotonicity in Young Graph and Thoma Theorem.” International Mathematics Research Notices (March 2015): rnv085 © 2015 The Author(s)