相关论文: The Janson inequalities for general up-sets

We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…

A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about…

Let $T$ be a tournament with nondecreasing score sequence $R$ and $A$ be its tournament matrix. An upset of $T$ corresponds to an entry above the main diagonal of $A$. Given a feasible score sequence $R$, Fulkerson~(1965) gave a simple…

The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…

For a multipartite correlation experiment with an arbitrary number of settings and any spectral type of outcomes at each site, we introduce a single general representation incorporating in a unique manner all Bell-type inequalities for…

In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using…

Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…

In this expository note we present simple proofs of the lower bound of Ramsey numbers (Erd\"os theorem), and of the estimation of discrepancy. Neither statements nor proofs require any knowledge beyond high-school curriculum (except a minor…

The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of…

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…

The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Pe\~{n}a, Pinelis and van de Geer. Moreover,…

Ruzsa's equivalence theorem provided a framework for converting certain families of inequalities in additive combinatorics to entropic inequalities (which sometimes did not possess stand-alone entropic proofs). In this work, we first…

We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…

In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial…

The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…

In 2010, Cilleruelo, Ruzsa, and Vinuesa established a surprising connection between the maximum possible size of a generalized Sidon set in the first $N$ natural numbers and the optimal constant in an ``analogous'' problem concerning…

In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…

For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…

In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.