Chen, Xia
Precise intermittency for the parabolic Anderson equation with an (1+1)-dimensional time–space white noise
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4 , p. 1486-1499
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MR 3414455
doi : 10.1214/15-AIHP673
URL stable : http://www.numdam.org/item?id=AIHPB_2015__51_4_1486_0

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.
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.

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