Bernoulli

  • Bernoulli
  • Volume 10, Number 5 (2004), 755-782.

Transportation of measure, Young diagrams and random matrices

Gordon Blower

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Abstract

The theory of transportation of measure for general convex 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. There are applications to the Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N→∞ and to the mean-field theory of random matrices. For the potential logΓ(x+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution are shown to satisfy a Gaussian concentration-of-measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matrix size increases; the limiting density is given by the derivative of the Vershik probability density.

Article information

Source
Bernoulli, Volume 10, Number 5 (2004), 755-782.

Dates
First available in Project Euclid: 4 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1099579155

Digital Object Identifier
doi:10.3150/bj/1099579155

Mathematical Reviews number (MathSciNet)
MR2093610

Zentralblatt MATH identifier
1065.60014

Keywords
infinite symmetric group logarithmic Sobolev inequality Young tableau

Citation

Blower, Gordon. Transportation of measure, Young diagrams and random matrices. Bernoulli 10 (2004), no. 5, 755--782. doi:10.3150/bj/1099579155. https://projecteuclid.org/euclid.bj/1099579155


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