Related papers: Full expectation value statistics for randomly sam…
Let $A$ be a real skew-symmetric Gaussian random matrix whose upper triangular elements are independently distributed according to the standard normal distribution. We provide the distribution of the largest singular value $\sigma_1$ of…
An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
This paper primarily establishes an asymptotic variance estimate for smooth linear statistics associated with zero sets of systems of random holomorphic sections in a sequence of positive Hermitian holomorphic line bundles on a compact…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
This paper proposes an approach to interpreting quantum expectation values that may help address the quantum measurement problem. Quantum expectation values are usually calculated via Hilbert space inner products and, thereby, differently…
We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping…
We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
We consider an isolated macroscopic quantum system in a pure state $\psi_t$ evolving unitarily in a separable Hilbert space $\mathcal{H}$ and take for granted that different macro states $\nu$ correspond to mutually orthogonal subspaces…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We consider $N\times N$ Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions on the…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We introduce a spectral approach to characterizing the three-dimensional Edwards-Anderson spin glass. By analyzing the eigenvalue statistics of overlap matrices constructed from two-dimensional cross-sections, we identify a crossover from…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
We investigate the optimal estimation of quantum expectation value of a physical observable, which minimizes a mean error with respect to general measure of deviation, when a finite number of copies of a pure state are prepared. If pure…