Related papers: Eigenvalue distribution from bootstrap estimates
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…
Several applications of the moment method in random matrix theory, especially, to local eigenvalue statistics at the spectral edges, are surveyed, with emphasis on a modification of the method involving orthogonal polynomials.
Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently…
The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
We present a history-dependent Monte Carlo scheme for the efficient calculation of the free-energy of quantum systems, inspired by the Wang-Landau sampling and metadynamics method. When embedded in a path integral formulation, it is of…
Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix,…
This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve…
In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications…
In this article we propose a model based on the Statistical Bootstrap approach to estimate the cross sections of different hadronic reactions up to a few GeV in c.m.s energy. The method is based on the idea, when two particles collide a so…
We study simplified bootstrap problems for probability distributions on the infinite line and the circle. We show that the rapid convergence of the bootstrap method for problems on the infinite line is related to the fact that the smallest…
We consider the problem of quantifying uncertainty for the estimation error of the leading eigenvector from Oja's algorithm for streaming principal component analysis, where the data are generated IID from some unknown distribution. By…
This guide aims at providing a general introduction to bootstrap methods. By using simple examples taken from nuclear physics, I discuss how such a method can be used to quantify error bars of an estimator. I also investigate the use of…
We present a methodology for accelerating the estimation of the free energy from path integral Monte Carlo simulations by considering an intermediate artificial reference system where interactions are inexpensive to evaluate numerically.…
A variational approach for the free energy is used to study the three-dimensional anisotropic XY model in the presence of a crystal field. The magnetization and the phase diagrams as a function of the parameters of the Hamiltonian are…
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the…