Focusing Gibbs measures with harmonic potential

Tristan Robert; Kihoon Seong; Leonardo Tolomeo; Yuzhao Wang

Focusing Gibbs measures with harmonic potential

Tristan Robert, Kihoon Seong, Leonardo Tolomeo, Yuzhao Wang

Mathematics

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Abstract

In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr\"odinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption.

Original language	English
Publisher	Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Publication status	Published - 21 Dec 2023

Bibliographical note

31 pages

Keywords

math.PR
60H30, 81T08, 35Q55

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2212.11386v1

Cite this

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abstract = " In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr\{"}odinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption. ",

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AU - Robert, Tristan

AU - Seong, Kihoon

AU - Tolomeo, Leonardo

AU - Wang, Yuzhao

N1 - 31 pages

PY - 2023/12/21

Y1 - 2023/12/21

N2 - In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr\"odinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption.

AB - In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr\"odinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption.

KW - math.PR

KW - 60H30, 81T08, 35Q55

UR - https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques

M3 - Preprint

BT - Focusing Gibbs measures with harmonic potential

PB - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

ER -

Focusing Gibbs measures with harmonic potential

Abstract

Bibliographical note

Keywords

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