Related papers: Random Matrix Spectra from Boltzmann-Weighted Latt…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
The present work is dedicated to a better understanding of the stability properties of regularized lattice Boltzmann (LB) schemes. To this extent, linear stability analyses of two-dimensional models are proposed: the standard…
We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension…
Periodic band structures are a hallmark phenomenon of condensed matter physics. While often imposed by external potentials, periodicity can also arise through the interplay of couplings that are not necessarily spatially periodic on their…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and…
We present a lattice-based numerical method to describe the non equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical…
Recent advances in AdS/CFT holography have suggested that the near-horizon dynamics of black holes can be described by random matrix systems. We study how the energy spectrum of a system with a generic random Hamiltonian matrix affects its…