Optimal Cheeger cuts and bisections of random geometric graphsMay 22 2018Let $d \geq 2$. The Cheeger constant of a graph is the minimum surface-to-volume ratio of all subsets of the vertex set with relative volume at most 1/2. There are several ways to define surface and volume here: the simplest method is to count boundary ... More
Elements of the Kopula (eventological copula) theoryFeb 17 2018New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known ... More
Frechet bounds of the 1-st kind for sets of half-rare eventsFeb 10 2018Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on the analogous ... More
Capturing, Ordering and Gaussianity in 2DJan 19 2016We collect various facts related loosely to random Gaussian quadrilaterals in the plane. For example, a side of a degenerate quadrilateral (one point inside three others) has a density that is non-Rayleigh.
Expected n-Step Product for Gaussian ToursDec 17 2015Supplements to Mehta & Normand (1997) are given, with regard to integrals involving Euclidean distances between n+1 random points in d-dimensional space, each visited once.