Random matrices and permutations, matrix integrals and integrable systems
Random walk in a strongly inhomogeneous environment and invasion percolation
Random walks in a Dirichlet environment.
Randomly interacting particle systems : the uniqueness regime
Resonant delocalization for random Schrödinger operators on tree graphs
We analyse the spectral phase diagram of Schrödinger operators on regular tree graphs, with the graph adjacency operator and a random potential given by random variables. The main result is a criterion for the emergence of absolutely continuous spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials spectrum appears at arbitrarily weak disorder in an energy regime which extends beyond the spectrum of. Incorporating...
Rigorous solution of a mean field spin glass model.