Generative models based on diffusion have become the state of the art in the last few years,
notably for image generation. Here, we analyze them in the high-dimensional limit, where …

In this paper, we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP
model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We …

We study the spectral properties of the adjacency matrix in the giant connected component
of Erdös-Rényi random graphs, with average degree p and randomly distributed hop** …

We consider the static and the dynamic phases in a Rosenzweig-Porter (RP) random matrix
ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation …

A new paradigm of Anderson localization caused by correlations in the long-range hop**
along with uncorrelated on-site disorder is considered which requires a more precise …

We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice
models. Such networks can be diagonalized by a finite sequence of local unitary …

A central theoretical issue at the core of the current research on many-body localization
(MBL) consists in characterizing the statistics of rare long-range resonances in many-body …

This paper proves universality of the distribution of the smallest and largest gaps between
eigenvalues of generalized Wigner matrices, under some smoothness assumption for the …

In this paper we give a physically transparent picture of singular-continuous spectrum in
disordered systems which possess a non-ergodic extended phase. We present a simple …

We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter
model, which is known to possess three distinct phases: ergodic, multifractal and localized …