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A Binomial Splitting Process in Connection with Corner Parking Problems

Part of: Limit theorems Combinatorial probability Algorithms - Computer Science

Published online by Cambridge University Press:  30 January 2018

Michael Fuchs ,
Hsien-Kuei Hwang ,
Yoshiaki Itoh  and
Hosam H. Mahmoud
Michael Fuchs*
Affiliation:
National Chiao Tung University
Hsien-Kuei Hwang*
Affiliation:
Academia Sinica
Yoshiaki Itoh*
Affiliation:
Institute of Statistical Mathematics
Hosam H. Mahmoud*
Affiliation:
The George Washington University
*
∗ Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan. Email address: mfuchs@math.nctu.edu.tw
∗∗ Postal address: Institute of Statistical Science and Institute of Information Science, Academia Sinica, Taipei, 115, Taiwan.
∗∗∗ Postal address: Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan.
∗∗∗∗ Postal address: Department of Statistics, The George Washington University, Washington, DC 20052, USA.
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Abstract

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This paper studies a special type of binomial splitting process. Such a process can be used to model a high dimensional corner parking problem as well as determining the depth of random PATRICIA (practical algorithm to retrieve information coded in alphanumeric) tries, which are a special class of digital tree data structures. The latter also has natural interpretations in terms of distinct values in independent and identically distributed geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by a logarithmic mean and a bounded variance, which is oscillating, if the binomial parameter p is not equal to ½, and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.

Keywords

Binomial distributionparking problemperiodic fluctuationasymptotic approximationdigital treede-Poissonization

MSC classification

Primary: 60C05: Combinatorial probability 68W40: Analysis of algorithms
Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 971 - 989
Copyright
© Applied Probability Trust 

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