This paper is a first attempt to describe the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which provides precise information on the structure of such a word. With each Sturmian word of slope α, we associate particular sequences of factor lengths which have a given “position” with respect to the sequence of continuants of α...

This paper describes work carried out to develop a method for considering actual traffic loads during bridge evaluation. This method is based on the use of load correction factors which have been determined using a probabilistic analysis of bridge loads and resistance. Load correction factors are selected as a function of site characteristics and used in order to modify load effects calculated ...

In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable capacities. This model was introduced by Kazemi in 2012. We obtain the mean and variance of the first Zagreb index and introduce a martingale based on this quantity.

Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called “Count”, which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further probabilistic analysis of “Count”. We derive an exact formula for the average number of swaps needed by “Count” as well as an asymptotic formula for the varia...

A recommendation system tracks past actions of a group of users to make recommendations to individual members of the group. The growth of computer-mediated marketing and commerce has led to increased interest in such systems. We introduce a simple analytical framework for recommendation systems, including a basis for defining the utility of such a system. We perform probabilistic analyses of al...

In this note we provide a simpler proof of a probabilistic analysis of the set cover problem given in [6]. We also prove these results using the language of high probability instead of using convergence in probability or convergence almost everywhere, making the previous results more precise.