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Variations-Matching-Problem.pdf (322.85 KB)
ETD Abstract Container
Abstract Header
Variations on the Matching Problem
Author Info
Judkovich, David
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1554308993793382
Abstract Details
Year and Degree
2019, Master of Sciences, Case Western Reserve University, Mathematics.
Abstract
We consider two extensions of the matching problem of classical combinatorial probability. We first consider the number of approximate matches in a randomly chosen permutation; an element is called an approximate match if it is within c of its original position. We also consider the distribution of the number of k-cycles of a random permutation and, more generally, a permutation conditioned to only contain cycles of length not exceeding r. In both cases we prove that the distributions are approximately Poisson under suitable conditions and obtain bounds on the total variation distance between the distributions and their respective Poisson limiting distributions. The main technical tool used is Stein's method of exchangeable pairs.
Committee
Elizabeth Meckes (Advisor)
Mark Meckes (Committee Member)
Stanislaw Szarek (Committee Member)
Pages
41 p.
Subject Headings
Mathematics
Keywords
probability
;
steins method
;
poisson approximation
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Citations
Judkovich, D. (2019).
Variations on the Matching Problem
[Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1554308993793382
APA Style (7th edition)
Judkovich, David.
Variations on the Matching Problem.
2019. Case Western Reserve University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1554308993793382.
MLA Style (8th edition)
Judkovich, David. "Variations on the Matching Problem." Master's thesis, Case Western Reserve University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1554308993793382
Chicago Manual of Style (17th edition)
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Document number:
case1554308993793382
Download Count:
294
Copyright Info
© 2019, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.