Related papers: Exact Probability Bounds under Moment-matching Res…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the…
We prove an exponential deviation inequality for the convex hull of a finite sample of i.i.d. random points with a density supported on an arbitrary convex body in $\R^d$, $d\geq 2$. When the density is uniform, our result yields rate…
Stable matching is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new upper bound on…
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness $D_3$ is bounded from…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to random phenomena that exhibit diverging relative…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…