Asymptotic behavior of permutation records

Record-dependent measures on the symmetric groups

A probability measure Pn on the symmetric group Sn is said to be record-dependent if Pn(σ) depends only on the set of records of a permutation σ ∈ Sn. A sequence P = (Pn)n∈N of consistent recorddependent measures determines a random order on N. In this paper we describe the extreme elements of the convex set of such P . This problem turns out to be related to the study of asymptotic behavior of...

Martingales and Profile of Binary Search Trees

We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.

Multiway trees of Maximum and Minimum Probability under the Random Permutation Model

Multiway trees, also known as m-ary search trees, are data structures generalizing binary search trees. A common probability model for anlayzing the behavior of these structures is the random permutation model. The probability mass function Q on the set of m-ary search trees under the random permutation model is the distribution induced by sequentially inserting the records of a uniformly rando...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables

Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...