We show in this paper that the Plancherel measure of the symmetric group S n converges weakly (as n ! 1) to a Gaussian random process in the innnite dimensional vector space. With respect to the law… (More)

where Fk(M) = ∫ X fk(x)M(dx), the angle brackets denote the average in M , and f1, . . . , fm are the coordinates of a map f : X → R. The formula describes implicitly the joint distribution of the… (More)

The description of characters of the innnite symmetric group S1 = lim ?! Sn is considered in the paper as an asymptotical combinatorial problem. It is equivalent to the characterization problem of… (More)

The main purpose of this note is to prove a convolution formula for conjugacy classes in symmetric groups suggested in [7] (formula (2.2), see also [8]). Given a partition ρ ⊢ r of a positive integer… (More)

Λ:λրΛ(cα(b) + u)(cα(b) + v)κα(λ, Λ)φ(Λ) = (nα + uv) φ(λ), where cα(b) is the α-content of a new box b = Λ \ λ. If α = 1, this identity implies the existence of an interesting family of positive… (More)

Let C(n; N) = R H N tr Z 2n (dZ) denote a matrix integral by a U(N)-invariant gaussian measure on the space H N of hermitian N N matrices. The integral is known to be always a positive integer. We… (More)

The aim of this paper is to show that for a wide class of orthogonal poly-nomials (including the classical polynomials of Hermite, Laguerre and Jacobi) there is a common universal asymptotics of root… (More)