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November 2015 Precise intermittency for the parabolic Anderson equation with an $(1+1)$-dimensional time–space white noise
Xia Chen
Ann. Inst. H. Poincaré Probab. Statist. 51(4): 1486-1499 (November 2015). DOI: 10.1214/15-AIHP673

Abstract

The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an $(1+1)$-dimensional time–space white noise. Our main result positively confirms an open problem posted in (Ann. Probab. (2015) to appear) and originated from the observations made in the physical literature (J. Statist. Phys. 78 (1995) 1377–1401) and (Nuclear Physics B 290 (1987) 582–602). By a link through the Feynman–Kac’s formula, our theorem leads to the evaluation of the ground state energy for the $n$-body problem with Dirac pair interaction.

Nous calculons les moments de l’exposant de Lyapunov de la solution de l’équation d’Anderson parabolique avec un bruit blanc en espace–temps en dimension $(1+1)$. Notre résultat principal confirme un problème ouvert posé dans (Ann. Probab. (2015) à paraître) et basé sur des observations faites dans la littérature physique (J. Statist. Phys. 78 (1995) 1377–1401) et (Nuclear Physics B 290 (1987) 582–602). À travers la formule de Feynman–Kac, notre théorème permet l’évaluation de l’état fondamental pour le problème à $n$-corps avec interaction de Dirac par paires.

Citation

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Xia Chen. "Precise intermittency for the parabolic Anderson equation with an $(1+1)$-dimensional time–space white noise." Ann. Inst. H. Poincaré Probab. Statist. 51 (4) 1486 - 1499, November 2015. https://doi.org/10.1214/15-AIHP673

Information

Received: 13 December 2014; Revised: 23 February 2015; Accepted: 25 February 2015; Published: November 2015
First available in Project Euclid: 21 October 2015

zbMATH: 1333.60136
MathSciNet: MR3414455
Digital Object Identifier: 10.1214/15-AIHP673

Subjects:
Primary: 60F10, 60H15, 60H40, 60J65, 81U10

Rights: Copyright © 2015 Institut Henri Poincaré

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Vol.51 • No. 4 • November 2015
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