Results 1 
7 of
7
Onedimensional stochastic growth and Gaussian . . .
, 2005
"... In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit distribution functions coming from certain Gaussian ensembles of ..."
Abstract

Cited by 21 (9 self)
 Add to MetaCart
In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit distribution functions coming from certain Gaussian ensembles of random matrices. This connection can be explained via point processes associated to the PNG model and the random matrices ensemble by an extension to the multilayer PNG and multimatrix models, respectively. We also discuss other models which are equivalent to the PNG model: directed polymers, the longest increasing subsequence problem, Young tableaux, a directed percolation model, kinkantikink gas, and Hammersley process.
Jack deformations of Plancherel measures and traceless Gaussian random matrices
, 2008
"... We study random partitions λ = (λ1, λ2,..., λd) of n whose length is not bigger than a fixed number d. Suppose a random partition λ is distributed according to the Jack measure, which is a deformation of the Plancherel measure with a positive parameter α> 0. We prove that for all α> 0, in the ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We study random partitions λ = (λ1, λ2,..., λd) of n whose length is not bigger than a fixed number d. Suppose a random partition λ is distributed according to the Jack measure, which is a deformation of the Plancherel measure with a positive parameter α> 0. We prove that for all α> 0, in the limit as n → ∞, the joint distribution of scaled λ1,..., λd converges to the joint distribution of some random variables from a traceless Gaussian βensemble with β = 2/α. We also give a short proof of Regev’s asymptotic theorem for the sum of βpowers of f λ, the number of standard tableaux of shape λ.
CORRELATION KERNELS FOR DISCRETE SYMPLECTIC AND ORTHOGONAL ENSEMBLES
, 712
"... Abstract. In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlatio ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
Abstract. In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlation kernels associated to the classical Meixner and Charlier weights. Contents
MATRIX KERNELS FOR MEASURES ON PARTITIONS
, 2008
"... We consider the problem of computation of the correlation functions for the zmeasures with the deformation (Jack) parameters 2 or 1/2. Such measures on partitions are originated from the representation theory of the infinite symmetric group, and in many ways are similar to the ensembles of Random ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
We consider the problem of computation of the correlation functions for the zmeasures with the deformation (Jack) parameters 2 or 1/2. Such measures on partitions are originated from the representation theory of the infinite symmetric group, and in many ways are similar to the ensembles of Random Matrix Theory of β = 4 or β = 1 symmetry types. For a certain class of such measures we show that correlation functions can be represented as Pfaffians including 2 ×2 matrix valued kernels, and compute these kernels explicitly. We also give contour integral representations for correlation kernels of closely connected measures on partitions.