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December, 2020 On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors
Michael Fuchs, Louis Kao, Wan-Zhen Wu
Taiwanese J. Math. 24(6): 1353-1382 (December, 2020). DOI: 10.11650/tjm/200503


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.


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Michael Fuchs. Louis Kao. Wan-Zhen Wu. "On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors." Taiwanese J. Math. 24 (6) 1353 - 1382, December, 2020.


Received: 30 October 2019; Revised: 20 March 2020; Accepted: 21 May 2020; Published: December, 2020
First available in Project Euclid: 19 November 2020

MathSciNet: MR4176877
Digital Object Identifier: 10.11650/tjm/200503

Primary: 05A16 , 60C05 , 68W40

Keywords: asymptotics , displacement cost , generating functions , Laplace method , sensor

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 6 • December, 2020
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