A simple construction of the Anderson operator via its quadratic form in dimensions two and three
Year: 2025
Type: article
Abstract: We provide a simple construction of the Anderson operator in dimensions two and three. This is done through its quadratic form. We rely on an exponential transform instead of the regularity structures or paracontrolled calculus which are usually used for the construction of the operator. The knowledge of the form is robust enough to deduce important properties such as positivity and irreducibility of the corresponding semigroup. The latter property gives existence of a spectral gap.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.712
Authors: Antoine Mouzard, El Maati Ouhabaz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408829427