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 limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribu...

Motivated by original Skorokhod's ideas, a new topology has been deened on the space P(X) of tight probability distributions on a topological space (X;). The only topological assumption imposed on (X;) is that some countable family of continuous functions separates points of X. This new sequential topology, deened by means of a variant of the a.s. Skorokhod representation, is quite operational ...

Determining convergence of Monte Carlo criticality problems is complicated by the statistical noise inherent in the random walks of the neutrons in each generation. The latest version of MCNP5 incorporates an important new tool for assessing convergence: the Shannon entropy of the fission source distribution, Hsrc. Shannon entropy is a well-known concept from information theory and provides a s...

$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...