Taiwanese Journal of Mathematics

On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors

Michael Fuchs, Louis Kao, and Wan-Zhen Wu

Advance publication

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Abstract

We re-visit the asymptotics of a binomial and a Poisson sum which arose as (average) displacement costs when moving randomly placed sensors to anchor positions. The first-order asymptotics of these sums were derived in several stages in a series of recent papers. In this paper, we give a unified approach based on the classical Laplace method with which one can also derive more terms in the asymptotic expansions. Moreover, in a special case, full asymptotic expansions can be given which even hold as identities. This will be proved by a combinatorial approach and systematic ways of computing all coefficients of these identities will be discussed as well.

Article information

Source
Taiwanese J. Math., Advance publication (2020), 30 pages.

Dates
First available in Project Euclid: 28 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1590652820

Digital Object Identifier
doi:10.11650/tjm/200503

Subjects
Primary: 05A16: Asymptotic enumeration 60C05: Combinatorial probability 68W40: Analysis of algorithms [See also 68Q25]

Keywords
sensor displacement cost asymptotics Laplace method generating functions

Citation

Fuchs, Michael; Kao, Louis; Wu, Wan-Zhen. On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors. Taiwanese J. Math., advance publication, 28 May 2020. doi:10.11650/tjm/200503. https://projecteuclid.org/euclid.twjm/1590652820


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