Random centers of localization for random operators

TL;DR

This paper introduces a novel random process for constructing eigenvectors of certain random operators, linking the process to the resolvent, by randomly selecting the localization center.

Contribution

It presents a new method for eigenvector construction in random operators, emphasizing the role of random localization centers, which is a novel approach.

Findings

Establishes a connection between the new process and the resolvent.

Provides a simplified and elegant framework for eigenvector construction.

Highlights the importance of random localization centers in spectral analysis.

Abstract

We propose a new random process to construct the eigenvectors of some random operators which make a short and clean connection with the resolvent. In this process the center of localization has to be chosen randomly.