The spectrum of local random Hamiltonians

Abstract

The spectrum of a local random Hamiltonian can be represented generically by the so-called $\epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $\epsilon$-noncrossing partitions and permutations to study its spectrum. Moreover, we derive some lower and upper bounds for the largest eigenvalue of the Hamiltonian.

22 pages

References in corpus (1)

• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices

Cited by in corpus (1)

• Energy dynamics in a class of local random matrix Hamiltonians