Related papers: Random Matrix approach to collective behavior and …
A common task in physics, information theory, and other fields is the analysis of properties of subsystems of a given system. Given the covariance matrix $M$ of a system of $n$ coupled variables, the covariance matrices of the subsystems…
Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
Training neural networks with batch normalization and weight decay has become a common practice in recent years. In this work, we show that their combined use may result in a surprising periodic behavior of optimization dynamics: the…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities…
We analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
Proteins are made of atoms constantly fluctuating, but can occasionally undergo large-scale changes. Such transitions are of biological interest, linking the structure of a protein to its function with a cell. Atomic-level simulations, such…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
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…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed…
This work presents a detailed covariance and correlation matrix analysis for experimentally measured cross sections obtained using the activation technique. Both statistical and systematic contributions to the covariance matrix were…
The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure…
The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval $(0,1)$ of the real line respectively. The averaged value of the modulus of the corresponding…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…
We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…