Affiliation:
1. Klosterneuburg, A 3400, IST Austria
Abstract
We consider a Wigner-type ensemble, i.e. large hermitian [Formula: see text] random matrices [Formula: see text] with centered independent entries and with a general matrix of variances [Formula: see text]. The norm of [Formula: see text] is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of [Formula: see text] that substantially improves the earlier bound [Formula: see text] given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields 169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory
Reference10 articles.
1. Universality for general Wigner-type matrices
2. Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half-Plane
3. An Introduction to Random Matrices
4. D. B. Arnold and M. R. Sleep, Uniform Random Generation of Balanced Parenthesis Strings, ACM Transactions on Programming Languages and Systems (TOPLAS), Vol. 2.1 (1980), pp. 122–128.
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