On Weighted Depths in Random Binary Search Trees
Rafik, Aguech . 2017
Following the model introduced by Aguech et al. (Probab Eng Inf Sci 21:133–141, 2007), the weighted depth of a node in a labelled rooted tree is the sum of all labels on the path connecting the node to the root. We analyse weighted depths of nodes with given labels, the last inserted node, nodes ordered as visited by the depth first search process, the weighted path length and the weighted Wiener index in a random binary search tree. We establish three regimes of nodes depending on whether the second-order behaviour of their weighted depths follows from fluctuations of the keys on the path, the depth of the nodes or both. Finally, we investigate a random distribution function on the unit interval arising as scaling limit for weighted depths of nodes with at most one child.
In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some…
In this paper, we give some results about a multi-drawing urn with random
addition matrix. The process that we study is described as: at stage n ≥ 1,
we pick out at random…
I
In this article, we consider several models of random walks in one or several
dimensions, additionally allowing, at any unit of time, a reset (or “catastrophe”) of
the walk…