MOUZARD, Antoine; OUHABAZ, El Maati

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MOUZARD, Antoine
Département de Mathématiques et Applications - ENS-PSL [DMA]

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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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.< Réduire

Mots clés en anglais

Anderson form

singular stochastic operator

Schrödinger operator

renormalization

positivity

spectral gap

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

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Résumé en anglais

Mots clés en anglais

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