A simple construction of the Anderson operator via its quadratic form in dimensions two and three
| hal.structure.identifier | Département de Mathématiques et Applications - ENS Paris [DMA] | |
| dc.contributor.author | MOUZARD, Antoine | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:33:20Z | |
| dc.date.available | 2024-04-04T02:33:20Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190468 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Anderson form | |
| dc.subject.en | singular stochastic operator | |
| dc.subject.en | Schrödinger operator | |
| dc.subject.en | renormalization | |
| dc.subject.en | positivity | |
| dc.subject.en | spectral gap | |
| dc.title.en | A simple construction of the Anderson operator via its quadratic form in dimensions two and three | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.identifier.arxiv | 2309.02821 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04197062 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04197062v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=MOUZARD,%20Antoine&OUHABAZ,%20El%20Maati&rft.genre=preprint |
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