Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence

Abstract

The mini-workshop was devoted to the spectral analysis of random Schrödinger-type operators. While this topic has been intensively studo ied by physicists and mathematicians for several decades, more recently there has been particular attention devoted to models where the random parameters enter the model in a non-monotone or non-linear way. Most of the established methods applied for random operators, in fact, hinge on the presence of monotonicity w. r. t. randomness. Thus the treatment of non-monotone models forces a deeper analysis of the structure of random Hamiltonians and, in particular, the interplay of the kinetic and the potential energy parts.