Related papers: Spectral properties of the trap model on sparse ne…
We study a microscopic mean-field model for the dynamics of the electron glass, near a local equilibrium state. Phonon-induced tunneling processes are responsible for generating transitions between localized electronic sites, which…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
In this work, we study the dynamics of complex systems with time-dependent transition rates, focusing on $p$-adic analysis in modeling such systems. Starting from the master equation that governs the stochastic dynamics of a system with a…
We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain…
We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We perform a…
We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate…
Densification and sparsification of temporal networks are attributed to two fundamental mechanisms: a change in the population in the system and/or a change in the chances that nodes in the system are connected. In theory, each of these…
The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law…
The increasing availability of time --and space-- resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world datasets can often…
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…
At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show…
We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues…
We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the…
Optical micro-manipulation and trapping of micro-particles delivers a mechanical system in direct interaction with a beam of light. In this interaction, the optical properties such as polarisation, beam profile and wavelength of the…
This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times…