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Large language models have demonstrated remarkable capabilities in complex mathematical reasoning tasks, but they inevitably generate errors throughout multi-step solutions. Process-level Reward Models (PRMs) have shown great promise by…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order…
Perturbation theory of large-scale structures of the Universe at next-to-leading order and next-to-next-to-leading order provides us with predictions of cosmological statistics at sub-percent level in the mildly non-linear regime. Its use…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type.…
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…
We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity…
Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures to be given by…
A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix…
Random matrix theory, which characterizes spectral distributions of infinitely large matrices, plays a central role across diverse fields, including high-dimensional data analysis, ecology, neuroscience, and machine learning. Among its key…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical…
We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point…
Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) is an important technique to solve PWM problems, which control the output voltage of an inverter via selecting appropriate switching angles. Based on the Rational Univariate…
We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form…