Gaps in discrete random samples: extended abstract

Gaps in discrete random samples: extended abstract

Motivated by applications in enumerative combinatorics and the analysis of algorithms we investigate the number of gaps and the length of the longest gap in a discrete random sample from a general distribution. We obtain necessary and sufficient conditions on the underlying distribution for the gaps to vanish asymptotically (with probability 1, or in probability), and we study the limiting dist...

Gaps in Discrete Random Samples

Let (Xi)i∈N be a sequence of independent and identically distributed random variables with values in the set N0 of non-negative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1, . . . , Xn} of the first n values. We obtain necessary and sufficient conditions in terms of ...

Random Cayley Digraphs and the Discrete Logarithm (Extended Abstract)

Gaps in samples of geometric random variables

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be...

Random Triangulations ( Extended Abstract )

Let Tn denote the set of triangulations of a convex polygon K with n sides. We study functions that measure very natural \geometric" features of a triangulation 2 Tn, for example n( ) which counts the maximal number of diagonals in incident to a single vertex of K. It is familiar that Tn is bijectively equivalent to Bn, the set of rooted binary trees with n 2 internal nodes, and also to Pn, the...