A binomial splitting process in connection with corner parking problems
Probability
2013-11-27 v2
Abstract
A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The later also has natural interpretations in terms of distinct values in iid geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by logarithmic mean and bounded variance, which is oscillating, if the binomial parameter is not equal to 1/2, and asymptotic to 1 in the unbiased case. Also, the limiting distribution does not exist owing to periodic fluctuations.
Cite
@article{arxiv.1307.5610,
title = {A binomial splitting process in connection with corner parking problems},
author = {Michael Fuchs and Hsien-Kuei Hwang and Yoshiaki Itoh and Hosam H. Mahmoud},
journal= {arXiv preprint arXiv:1307.5610},
year = {2013}
}
Comments
20 pages