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, pp. 1486-1499.

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.

DOI : 10.1214/15-AIHP673
Mots-clés : intermittency, White noise, brownian motion, parabolic Anderson model, Feynman–Kac’s representation, ground state energy 
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     title = {Precise intermittency for the parabolic {Anderson} equation with an $(1+1)$-dimensional time{\textendash}space white noise},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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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, pp. 1486-1499. doi : 10.1214/15-AIHP673. http://www.numdam.org/articles/10.1214/15-AIHP673/

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