First-passage properties underlie a wide range of stochastic processes, such as diffusion-
limited growth, neuron firing, and the triggering of stock options. This book provides a unified …

The article reviews the physics of Anderson localization on random regular graphs (RRG)
and its connections to many-body localization (MBL) in disordered interacting systems …

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in
the Anderson model on random regular graphs (RRG) are studied. We consider the critical …

The interplay between disorder and quantum interference leads to a wide variety of physical
phenomena including celebrated Anderson localization—the complete absence of diffusive …

The study of matter fields on an ensemble of random geometries is a difficult problem still in
need of new methods and ideas. We will follow a point of view inspired by probability theory …

We investigate the dynamic properties of elastic lattices defined by tessellations of a curved
hyperbolic space. The lattices are obtained by our projecting nodes of a regular hyperbolic …

For Anderson localization on the Cayley tree, we study the statistics of various observables
as a function of the disorder strength W and the number N of generations. We first consider …

The self-organized criticality in Ehrenfest's historical dog-flea model is analyzed by
simulating the underlying stochastic process. The fluctuations around the thermal …

Hyperbolic lattices are starting to be explored in search of novel phases of matter. At the
same time, non-Hermitian physics has come to the forefront in photonic, optical, phononic …

The exact analytic expression for the mean time to trap** (or mean walklength) for a
particle (electron/exciton) performing a random walk on a finite dendrimer lattice with a trap …