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Thesis.pdf (1.41 MB)
ETD Abstract Container
Abstract Header
Spanning k-Trees and Loop-Erased Random Surfaces
Author Info
Parsons, Kyle
ORCID® Identifier
http://orcid.org/0000-0002-5064-3157
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1499871174299693
Abstract Details
Year and Degree
2017, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
We introduce a novel model of random hypersurfaces that generalizes loop-erased random walk. Using a duality with loop-erased random walk we show that if these surfaces have a growth exponent α then 2 < α ≤ 8/3 in three dimensions. We further present numerical evidence from experiment that the growth exponent is 2.5269 ± 0.0017 in 3 dimensions. The behavior is very different in d ≥ 4 dimensions where we show that this growth exponent exists and is d. We also study the dimension 1 homology of 2-dimensional random acyclic complexes chosen approximately uniformly. We present numerical evidence that this model of a random group is distributed according to the Cohen–Lenstra heuristics.
Committee
Matthew Kahle (Advisor)
Michael Davis (Committee Member)
John Lafont (Committee Member)
Pages
61 p.
Subject Headings
Mathematics
Keywords
loop-erased random walk
;
spanning trees
;
homology
;
acyclic
;
cohen--lenstra
;
duality
;
mathematics
;
combinatorics
;
topology
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RIS
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Citations
Parsons, K. (2017).
Spanning k-Trees and Loop-Erased Random Surfaces
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499871174299693
APA Style (7th edition)
Parsons, Kyle.
Spanning k-Trees and Loop-Erased Random Surfaces.
2017. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1499871174299693.
MLA Style (8th edition)
Parsons, Kyle. "Spanning k-Trees and Loop-Erased Random Surfaces." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499871174299693
Chicago Manual of Style (17th edition)
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Document number:
osu1499871174299693
Download Count:
420
Copyright Info
© 2017, some rights reserved.
Spanning k-Trees and Loop-Erased Random Surfaces by Kyle Parsons is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.