Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

@article{Oh2021OptimalIT,
  title={Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus},
  author={Tadahiro Oh and Philippe Sosoe and Leonardo Tolomeo},
  journal={Inventiones mathematicae},
  year={2021}
}
We study an optimal mass threshold for normalizability of the Gibbs measures associated with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional torus. In an influential paper, Lebowitz et al. (J Stat Phys 50(3–4):657–687, 1988) proposed a critical mass threshold given by the mass of the ground state on the real line. We provide a proof for the optimality of this critical mass threshold. The proof also applies to the two-dimensional radial problem posed on the unit… 

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