Related papers: Glassy Random Matrix Models
Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…
We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We investigate the slow dynamics of a colloidal model with two repulsive length scales, whose interaction potential is the sum of a hard-core and a square shoulder. Despite the simplicity of the interactions, Mode-Coupling theory predicts a…
Using molecular dynamics simulations we study the temperature-density phase diagram of a simple model system of particles in two dimensions. In addition to translational degrees of freedom, each particle has two internal states and…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain…
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…
We present a simple lattice model showing a glassy behavior. $R$ matrix analysis predicts critical termination of the super-cooled fluid branch at density $\rho_g=0.1717$. This prediction is confirmed by dynamical numerical simulations,…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
Glasses offer a broad range of tunable thermophysical properties that are linked to their compositions. However, it is challenging to establish a universal composition-property relation of glasses due to their enormous composition and…
A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We use computer simulation to investigate the topology of the potential energy $V(\{{\bf R}\})$ and to search for doublewell potential's (DWP) in a model glass . By a sequence of Newtonian and dissipative dynamics we find different minima…
The emergence of nanoscience has increased the importance of experiments able to probe the very local structure of materials, especially for disordered and heterogeneous systems. This is technologically important; for example, the nanoscale…