Related papers: Dominating Points of Gaussian Extremes
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variable satisfying a ``Ehrhard-like'' property for its…
With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known…
If $p:\mathbb{C} \to \mathbb{C}$ is a non-constant polynomial, the Gauss--Lucas theorem asserts that its critical points are contained in the convex hull of its roots. We consider the case when $p$ is a random polynomial of degree $n$ with…
Given n (discrete or continuous) random variables X_i, the (2^n-1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X_1,...,X_n} is called an entropic vector. Determining the region of entropic…
For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
In this paper, we consider projection estimates for L\'evy densities in high-frequency setup. We give a unified treatment for different sets of basis functions and focus on the asymptotic properties of the maximal deviation distribution for…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning Random Matrix Theory and the generalisation of the Tracy-Widom…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
This paper deals with the generalized convolutions connected with the Williamson transform and the maximum operation. We focus on such convolutions which can define transition probabilities of renewal processes. They should be monotonic…