Exact asymptotics in a mean field model with random potential
For a mean field operator with a random potential, asymptotic properties of the eigenvalues and eigenfunctions are studied and applied to investigate the long term behavior of the solutions of a corresponding large system of differential equations. The total mass of the system is approximately concentrated in the record point of the random potential (complete localization). A more detailed inspection of the peaks shows that there is a phase transition: Only in the case of a moderate increase of time relatively to the growth of the space size the model behaves similarly as the system without ``diffusion''. But also in the non- moderate case the asymptotic height of peaks can exactly be described.
mean field operator with a random potential
scientific article; zbMATH DE number 4109812
scientific article