相关论文: The Janson inequalities for general up-sets
The possibility to study intermittency in a single event of high multiplicity is investigated in the framework of the $\alpha-$model. It is found that, for cascade long enough, the dispersion of intermittency exponents obtained from…
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and…
The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a…
We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
Several years ago the authors started looking at some problems of convex geometry from a more general point of view, replacing volume by an arbitrary measure. This approach led to new general properties of the Radon transform on convex…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
We introduce two new concepts designed for the study of empirical processes. First, we introduce a new Orlicz norm which we call the Bernstein-Orlicz norm. This new norm interpolates sub-Gaussian and sub-exponential tail behavior. In…
For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…
The document tries to put focus on sequences with certain properties and periods leading to the first value smaller than the starting value in the Collatz problem. With the idea that, if all starting numbers lead ultimately to a smaller…
We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex…
Proofs of Bell's theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell's inequality holds identically for…
The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that…
Rare events can potentially occur in many applications. When manifested as opportunities to be exploited, risks to be ameliorated, or certain features to be extracted, such events become of paramount significance. Due to their sporadic…
A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
Given a random process $x(\tau)$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution ${\cal P}(x)$, we consider a sequence of dynamical observables $A_1, \dots, A_n$ associated to the…