Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators

TL;DR

This paper explores the equidistribution and unique continuation properties of eigenfunctions of Schrödinger and elliptic operators, reviewing recent advances and presenting new theoretical results.

Contribution

It introduces new equidistribution estimates and eigenvalue bounds for random Schrödinger operators, expanding understanding of eigenfunction behavior.

Findings

New equidistribution estimates for eigenfunctions

Eigenvalue bounds for random operators

Enhanced understanding of unique continuation principles

Abstract

We discuss properties of $L^2$-eigenfunctions of Schr\"odinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce new ones.