Related papers: Exact correlators in the Gaussian Hermitian matrix…
This work introduces non-Hermitian position-dependent mass Hamiltonians characterized by complex ladder operators and real, equidistant spectra. By imposing the Heisenberg-Weyl algebraic structure as a constraint, we derive the…
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into…
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…
The Jucys-Murphy elements for wreath products G_n associated to any finite group G are introduced and they play an important role in our study on the connections between class algebras of G_n for all n and vertex algebras. We construct an…
In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously…
We prove that the logarithm of the determinant of a Wigner matrix satisfies a central limit theorem in the limit of large dimension. Previous results about fluctuations of such determinants required that the first four moments of the matrix…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
We propose a novel parametrization of Cumulative Prospect Theory (CPT), as developed by Daniel Kahneman and Amos Tversky, that yields an explicit gamble valuation formula for Gaussian reward distributions. Specifically, we define parametric…
The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for $H=A+V$, where $A$ is the base matrix and $V$ is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of…
We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the moments are proportional to n to the power 2/3. We show that…
We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta…
We consider the elliptic Ginibre matrices in the orthogonal symmetry class that interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We obtain the finite size corrections of the real eigenvalue densities in…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is…
We investigate the super high-order Virasoro 3-algebra. By applying the appropriate scaling limits on the generators, we obtain the super $w_{\infty}$ 3-algebra which satisfies the generalized fundamental identity condition. We also define…
This paper establishes the relation between traditional results from (euclidean) twistor theory and chiral formulations of General Relativity (GR), especially the pure connection formulation. Starting from a $SU(2)$-connection only we show…
The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…
This paper is devoted to the phenomenon of superintegrability. This phenomenon is manifested in the existence of a formula for character averages, expressed through the same characters at special points and of its various generalization. In…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
The method of constrained Hamiltonian systems can be used to reduce Fock modules. It is applied to the Virasoro algebra, where a possibly new realization is found.