We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate shape of bumping route (in vicinity $y$-axis) when specified number is inserted into large Plancherel-distributed tableau. show that after projective change coordinate system converges in distribution Poisson process.

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete set of finitely supported eigenfunctions.

We introduce the concept of a modulator, which leads to a family of character formulae, each generalizing the Kirillov formula. For a suitable choice of modulator, this enables one to understand the Plancherel measure of a compact Lie group as arising from a partition of the identity on the dual of its Lie algebra.

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order n. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.

We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions. The Meixner ensemble is related to a two-dimensional directed growth model, and the Charlier ensemble is related to the...

Zero biasing for the normal approximation of a random variable W using Stein’s method was introduced in Goldstein and Reinert [16]. One instance in which the zero bias method may be applied is for W for which a Stein pair W,W ′ may be constructed, that is, for W that may be coupled to a variable W ′ such that W,W ′ is exchangeable and satisfies E(W ′|W ) = (1− a)W for some a ∈ (0, 1]. After giv...