Transportation of measure, Young diagrams and random matrices

Spectral Measure of Large Random Hankel, Markov and Toeplitz Matrices

We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {Xk} of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables {Xij}j>i of zero mean and unit variance, scaling the eigenvalues by √ n we prove the almost sure, weak convergence of the spectr...

Spectral Measure of Heavy Tailed Band and Covariance Random Matrices

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure μ̂ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N ×N symmetric matrix YσN whose (i, j) entry is σ( i N , j N )xij where (xij , 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-...

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

Gaussian fluctuations of Young diagrams under the Plancherel measure

We obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the ‘spectrum’ of partitions lwn2N (under the Plancherel measure), thus settling a long-standing problem posed by Logan & Shepp. Namely, under normalization growing like ffiffiffiffiffiffiffiffiffiffi log n p , the corresponding random process in the bulk is shown to converge, in the s...

Random 3-D Young Diagrams and Representation Theory