TY - JOUR

T1 - Transportation of measure, Young diagrams and random matrices.

AU - Blower, Gordon

PY - 2004

Y1 - 2004

N2 - The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality. The are applications to Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N tends to infinity and to the mean field theory of random matrices. For the portential Gamma (N+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution satisfy a Gaussian concentration of measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matix size increases; the limiting density is given by the derivative of the Vershik probability density.

AB - The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality. The are applications to Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N tends to infinity and to the mean field theory of random matrices. For the portential Gamma (N+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution satisfy a Gaussian concentration of measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matix size increases; the limiting density is given by the derivative of the Vershik probability density.

KW - infinite symmetic group

KW - logarithmic Sobolev inequality

KW - Young tableaux

M3 - Journal article

VL - 10

SP - 755

EP - 782

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 5

ER -