Related papers: Exponential Order Statistics, the Basel problem an…
Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and $4$-regular partitions follow. In…
Schutzenberger's theorem for the ordinary RSK correspondence naturally extends to Chen et. al's correspondence for matchings and partitions. Thus the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) analytical formulas for the level spacing distribution…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…
It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential…
Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…
For a given wave function one can define a quantity $\mu_E$ having a meaning of its inverse spatial size. The Laplace transform of the distribution function $P(\mu_E)$ is calculated analytically for a 1D disordered sample with a finite…
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…
Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is…
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…
A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized)…
In this undergraduate thesis, we expand on the study of statistics on restricted growth functions avoiding patterns initiated by Campbell, et. al. Restricted growth functions are of interest because they are in bijection with set…
Protection of individual privacy is a common concern when releasing and sharing data and information. Differential privacy (DP) formalizes privacy in probabilistic terms without making assumptions about the background knowledge of data…
Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…