Related papers: Impurity models and products of random matrices
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic…
The thermodynamic, dynamic and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two dimensional associating lattice gas model that exhibits density…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The interplay between impurities and interactions is studied in the gapless phase of two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in single-chain model will be changed by…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by…
In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby.…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed…
This preprint is the introduction of my habilitation thesis for Paris7 university. It is a sumary of a collection of works on the 2 matrix model. In an introduction, 3 different and unequivalent definitions of matrix models are given…
Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and…