Central limit theorem for Gibbs measures associated with focusing NLS

We study the focusing Φ4-measure on the real line, namely, focusing Gibbs measure associated with the Schrödinger equation, initiated by Lebowitz, Rose, and Speer (1988). Through the process of taking the infinite volume limit, we analyze that the focusing Φ4-measure with appropriate scaling exhibits Gaussian fluctuation around scaled solitary waves, which are minimizers of the focusing Hamiltonian.

This talk is based on ongoing work with Philippe Sosoe (Cornell)