# Random characteristics for Wigner matrices

## TL;DR

This paper extends the random characteristics method to Wigner matrices with non-normal entries and provides a dynamic proof of the weak local semicircle law in the bulk spectrum.

## Contribution

It introduces a generalized approach for Wigner matrices and offers a new dynamic proof of the semicircle law without assuming normality.

## Key findings

- Extended random characteristics to broader Wigner matrices
- Provided a simple proof of the weak local semicircle law
- Validated the approach for non-normal entries

## Abstract

We extend the random characteristics approach to Wigner matrices whose entries are not required to have a normal distribution. As an application, we give a simple and fully dynamical proof of the weak local semicircle law in the bulk.