A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

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Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

In this paper, we consider electric vehicle charging facilities that offer various levels of service, i.e., charging rates, for varying prices such that rational users choose a level of service that minimizes the total cost to themselves including an oppor ...

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and stiffness coefficients ...

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The pr ...

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

Wyner's common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis ...

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then th ...

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...

Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

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On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Sensitivity to user mischaracterizations in electric vehicle charging

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

The multivariate Serre conjecture ring

Robust optimization of control parameters for WEC arrays using stochastic methods

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

The double exponential runtime is tight for 2-stage stochastic ILPs

A Functional Perspective on Information Measures

Secrecy by Design With Applications to Privacy and Compression

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Common Information Components Analysis

A hybrid collocation-perturbation approach for PDEs with random domains

Feedback and Common Information: Bounds and Capacity for Gaussian Networks

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Sub‐asymptotic motivation for new conditional multivariate extreme models

Strong convergence of multivariate maxima

On arithmetic progressions in symmetric sets in finite field model

Fractional extreme distributions

Distributional Robustness in Mechanism Design