Focusing Gibbs measures with harmonic potential

Tristan Robert, Kihoon Seong, Leonardo Tolomeo, Yuzhao Wang

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger 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 languageEnglish
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Publication statusAccepted/In press - 23 Dec 2022


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