Unique continuation properties for the continuous Anderson operator in dimension 2
Probability
2025-05-09 v1
Abstract
We consider singular continuous Anderson operators on closed manifolds of dimension 1 and 2, and prove a unique continuation property for its eigenfunctions using the theory of quasi-conformal mappings. We investigate its nodal set by proving that it is quasi-conformal to the nodal set of a Laplace eigenfunction and prove a Courant nodal theorem. We also present an application to control for singular operator in dimension 1.
Keywords
Cite
@article{arxiv.2505.04774,
title = {Unique continuation properties for the continuous Anderson operator in dimension 2},
author = {Nicolas Moench},
journal= {arXiv preprint arXiv:2505.04774},
year = {2025}
}