Related papers: On Critical Points for Gaussian Vectors with Infin…
We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the…
We prove the 3-dimensional Gaussian product inequality, i.e., for any real-valued centered Gaussian random vector $(X,Y,Z)$ and $m\in \mathbb{N}$, it holds that…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
Motivated by the vacuum selection problem of string/M theory, we study a new geometric invariant of a positive Hermitian line bundle $(L, h)\to M$ over a compact K\"ahler manifold: the expected distribution of critical points of a Gaussian…
In cosmological perturbation theory it is convenient to use the scalar, vector, tensor (SVT) basis as defined according to how these components transform under 3-dimensional rotations. In attempting to solve the fluctuation equations that…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
In this note, we will get the estimate of the expected distribution of critical values of Gaussian SU(2) random polynomials as the degree large enough. The result is a direct application of the Kac-Rice formula. The critical values will…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
In this paper, we establish a useful set of formulae for the $\sin\Theta$ distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the perturbation of the original matrix propagates into…
In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of $\star$-scale invariant fields -- a class of log-correlated Gaussian fields -- around their extremal points by characterising the law of the…
All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are…
In this paper we promote the idea of quantum critical lines ({\em inter alia} surfaces) as opposed to points. A quantum critical line obtains when criticality at zero temperature is extended over a continuum in a one-dimensional line. We…
A convenient approach to analyze spatial infinity is to use a cylinder representation $I$ and impose a gauge based on a congruence of conformal geodesics. This so-called conformal Gauss gauge comes along with the freedom to specify initial…
Saddle points of a vector logarithmic energy with a vector polynomial external field on the plane constitute the vector critical measures, a notion that finds a natural motivation in several branches of analysis. We study in depth the case…
The study of long wavelength scalar perturbations, in particular the existence of conserved quantities when the perturbations are adiabatic, plays an important role in e.g. inflationary cosmology. In this paper we present some new conserved…
Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.