Abstract: In this talk, I will discuss joint work with Partha Dey and Kay Kirkpatrick. I will discuss the infinite volume behaviour of a Gibbs measure associated to a version of the focusing DNLS defined on the discrete torus, with two parameters representing the inverse temperature and strength of the non linearity. In particular, we show that the limit of the log partition converges to an explicit limit, the measure undergoes a phase transition concerning a behaviour of the maximum of a typical function, there is a continuous curve that divides the parametric plane in to two regions corresponding to the subcritical and supercritical phases, and finally that in the subcritical phase, a function sampled from the measure converges to the massive Gaussian Free Field.
Phase transition for the Discrete Non Linear Schrödinger Equation (DNLS) in Three Dimensions and Higher.
16.01.2025 14:30 - 16:00
Organiser:
A. Carrance, W. Da Silva, K. Ryan
Location: