Anderson stochastic quantization equation
Hugo Eulry
- Fonction : Auteur
- PersonId : 1340718
- IdHAL : hugo-eulry
- ORCID : 0009-0001-9662-3063
Antoine Mouzard
- Fonction : Auteur
- PersonId : 182934
- IdHAL : antoine-mouzard
- ORCID : 0000-0003-2643-7932
Tristan Robert
- Fonction : Auteur
- PersonId : 748187
- IdHAL : tristan-robert
- ORCID : 0000-0003-1987-4536
Résumé
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the nonlinearity, we construct the random Gibbs measure as an absolutely continuous measure with respect to the law of the Anderson Gaussian Free Field for fixed realization of the spatial white noise. Then, when the initial data is distributed according to the Gibbs measure, we prove almost sure global well-posedness for the dynamics and invariance of the Gibbs measure.
Format du dépôt | Notice |
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Type de dépôt | Pré-publication, Document de travail |
Titre |
en
Anderson stochastic quantization equation
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Résumé |
en
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the nonlinearity, we construct the random Gibbs measure as an absolutely continuous measure with respect to the law of the Anderson Gaussian Free Field for fixed realization of the spatial white noise. Then, when the initial data is distributed according to the Gibbs measure, we prove almost sure global well-posedness for the dynamics and invariance of the Gibbs measure.
|
Auteur(s) |
Hugo Eulry
1
, Antoine Mouzard
2
, Tristan Robert
3
1
IRMAR -
Institut de Recherche Mathématique de Rennes
( 1096399 )
- Campus de Beaulieu, bâtiments 22 et 23,
263 avenue du Général Leclerc, CS 74205
35042 RENNES Cédex
- France
2
DMA -
Département de Mathématiques et Applications - ENS Paris
( 66 )
- 45 rue d'Ulm
75005 Paris
- France
3
IECL -
Institut Élie Cartan de Lorraine
( 211251 )
- Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01
- France
|
Date de publication |
2024-01-23
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Langue du document |
Anglais
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Domaine(s) |
|
arXiv Id | 2401.12742 |
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