A simple construction of the Anderson operator via its quadratic form in dimensions two and three

2023/09/06 by Antoine Mouzard, Mouzard, Antoine, El Maati Ouhabaz +1 · 4 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.02821

openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Cited by

• Standing waves of the Anderson-Gross-Pitaevskii equation
• Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation
• On domains of elliptic operators with distributional coefficients
• On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

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