Spectral theory of selfadjoint Hankel matrices.

Hankel Matrices in Coding Theory and Combinatorics

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...

Dimension-free Concentration Bounds on Hankel Matrices for Spectral Learning

Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution. These methods rely on a singular value decomposition of a matrix HS , called the Hankel matrix, that records the frequencies of (s...

Determinants of Hankel Matrices

The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.

Some Aspects of Hankel Matrices in Coding Theory and Combinatorics

Hankel matrices consisting of Catalan numbers have been analyzed by various authors. DesainteCatherine and Viennot found their determinant to be ∏ 1≤i≤j≤k i+j+2n i+j and related them to the Bender Knuth conjecture. The similar determinant formula ∏ 1≤i≤j≤k i+j−1+2n i+j−1 can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients (2m+1 m ) . Generalizing t...