Related papers: Relating $p$-adic eigenvalues and the local Smith …
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…
The character of an irreducible admissible representation of a $p$-adic reductive group is known to be a constant function in some neighborhood of any regular semisimple element $\gamma$ in the group. Under certain mild restrictions on…
We determine the maximal eigenvalue of the p-adic curvature transformations on Bruhat-Tits buildings, and we give an essentially optimal upper bound on the minimal non-zero eigenvalue of these transformations.
We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…
In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence…
We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…
Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and…
Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
For large random matrices $X$ with independent, centered entries but not necessarily identical variances, the eigenvalue density of $XX^*$ is well-approximated by a deterministic measure on $\mathbb{R}$. We show that the density of this…
In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution,…
Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of its elements of that matrix. Note that…
We study Hadamard's variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for…
We derive generalizations of the Cherednik-Macdonald constant term identities associated to root systems which depend, besides on the usual multiplicity function, symmetrically on two quasi-periods. They are natural analogues of the…
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ of dimensionality $mn$ in a Gaussian ensemble of random, complex pure states of the composite system. For a given dimensionality $m$ of the subsystem $A$,…
The positive interpoint distances of n=p+1>1 points in dimension p are equal if and only if their sample covariance matrix is a scalar multiple of the identity.