Related papers: Matrix Majorization in Large Samples with Varying …
The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of…
In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…
In this paper we describe some properties of companion matrices and demonstrate some special patterns that arise when a Toeplitz or a Hankel matrix is multiplied by a related companion matrix. We present a new condition, generalizing known…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
This paper studies majorization of high tensor powers of finitely supported probability distributions. Viewing probability distributions as a resource with majorization as a means of transformation corresponds to the resource theory of pure…
We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be…
As a primary contribution, we present a convergence theorem for stochastic iterations, and in particular, Q-learning iterates, under a general, possibly non-Markovian, stochastic environment. Our conditions for convergence involve an…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We present an alternative proof of asymptotic freeness of independent sample covariance matrices, when the dimension and the sample size grow at the same rate, by embedding these matrices into Wigner matrices of a larger order and using…
Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…
The possibility of using similarity transformations to alter dynamical entanglement growth in matrix-product-state simulations of quantum systems is explored. By appropriately choosing the similarity transformation, the entanglement growth…
Machine learning models that are developed with invariance to certain types of data transformations have demonstrated superior generalization performance in practice. However, the underlying mechanism that explains why invariance leads to…
Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states…
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
Let $\orig{A}$ be any matrix and let $A$ be a slight random perturbation of $\orig{A}$. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under…
In this paper we describe the alternative approach to the sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of a distribution of the argument maximum. For a centered…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…