Limit Distribution of Eigenvalues for Random Hankel and Toeplitz Band Matrices
نویسندگان
چکیده
منابع مشابه
Limit Distributions for Random Hankel, Toeplitz Matrices and Independent Products
For random selfadjoint (real symmetric, complex Hermitian, or quaternion self-dual) Toeplitz matrices and real symmetric Hankel matrices, the existence of universal limit distributions for eigenvalues and products of several independent matrices is proved. The joint moments are the integral sums related to certain pair partitions. Our method can apply to random Hankel and Toeplitz band matrices...
متن کاملBalanced Random Toeplitz and Hankel Matrices
Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is sca...
متن کاملFluctuations of eigenvalues for random Toeplitz and related matrices
Consider random symmetric Toeplitz matrices Tn = (ai−j) n i,j=1 with matrix entries aj , j = 0, 1, 2, · · · , being independent real random variables such that E[aj ] = 0, E[|aj |] = 1 for j = 0, 1, 2, · · · , (homogeneity of 4-th moments) κ = E[|aj |], and further (uniform boundedness) sup j≥0 E[|aj |] = Ck <∞ for k ≥ 3. Under the assumption of a0 ≡ 0, we prove a central limit theorem for line...
متن کاملSpectral 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...
متن کاملIrreducible Toeplitz and Hankel matrices
An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2009
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-009-0260-4