Scaling limits of the Bouchaud and Dean trap model on Parisi's tree in ergodic and aging time scales

Abstract

We take scaling limits of the Bouchaud and Dean trap model on Parisi's tree in time scales where the dynamics is either ergodic (close to equilibrium) or aging (far from equilibrium). These results follow from a continuity theorem formulated for a certain kind of process on trees, which we call a cascading jump evolution, defined in terms of a collection of jump functions, with a cascading structure given by the tree.

21 pages, 1 figure; changed formatting of previous version to that of the Journal of Mathematical Physics, where it will appear; there are a few, minor changes and corrections on the content as well