Related papers: An Information-Theoretic Proof of the Kac--Bernste…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
Bolthausen used a variation of Stein's method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character…
By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…
The famous Jacobian conjecture asks if a morphism $f:K[x,y]\to K[x,y]$ having an invertible Jacobian is invertible ($K$ is a characteristic zero field). We show that if one of the following three equivalent conditions is satisfied, then $f$…
Let $X$ be a countable discrete Abelian group containing no elements of order 2, $\alpha$ be an automorphism of $X$, $\xi_1$ and $\xi_2$ be independent random variables with values in the group $X$ and distributions $\mu_1$ and $\mu_2$. The…
The class of selfdecomposable distributions in free probability theory was introduced by Barndorff-Nielsen and the third named author. It constitutes a fairly large subclass of the freely infinitely divisible distributions, but so far…
This note considers a finite dimensional statistical model for the Calder\'on problem with piecewise constant conductivities. In this setting it is shown that injectivity of the forward map and its linearisation suffice to prove the…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
In this paper, we prove the cone theorem and the contraction theorem for pairs $(X, B)$, where $X$ is a normal variety and $B$ is an effective $\mathbb R$-divisor on $X$ such that $K_X+B$ is $\mathbb R$-Cartier.
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
Heyde proved that a Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear statistic given another. The present article is devoted to a group analogue of the Heyde theorem. We…
Let X be a second countable locally compact Abelian group. Let $\xi_1, \xi_2$ be independent random variables with values in the group X and distributions $\mu_1, \mu_2$ such that the sum $\xi_1+\xi_2$ and the difference $\xi_1-\xi_2$ are…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
In a previous paper (arXiv:1008.3661v1[quant-ph] 21 Aug 2010), we have given a purely logical proof of the Conway and Kochen Free Will theorem in QM: the freedom of the observer implies the freedom of the observed particle. Here we show…