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Random Graphs, Sandpile Groups, and ...

Yale University.

Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices./
Author:	Koplewitz, Shaked.
Description:	1 online resource (58 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355018264

Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices.
Koplewitz, Shaked.

Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices. - 1 online resource (58 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis studies Random Graph Theory and Random Matrix Theory. In random graph theory, we study various properties of random graphs, first in random bipartite graphs and later in Erdo&huml;s--Renyi random directed graphs. We use spectral graph theory as a means through which to study graphs, by examining their laplacian matrices and sandpile groups, as well as studying the property of coeulerianness.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355018264Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices.
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020 $a 9780355018264
035 $a (MiAaPQ)AAI10631631
035 $a AAI10631631
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Koplewitz, Shaked. $3 1180921
245 1 0 $a Random Graphs, Sandpile Groups, and Surjectivity of Random Matrices.
264 0 $c 2017
300 $a 1 online resource (58 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Sam Payne.
502 $a Thesis (Ph.D.) $c Yale University $d 2017.
504 $a Includes bibliographical references
520 $a This thesis studies Random Graph Theory and Random Matrix Theory. In random graph theory, we study various properties of random graphs, first in random bipartite graphs and later in Erdo&huml;s--Renyi random directed graphs. We use spectral graph theory as a means through which to study graphs, by examining their laplacian matrices and sandpile groups, as well as studying the property of coeulerianness.
520 $a In particular, we calculate the distribution of the p-rank of the sandpile group in random bipartite graphs. We also show that the asymptotic probability that an Erdo&huml;sRenyi random directed graph is coeulerian is bounded from above by a constant around 0.44.
520 $a In random matrices we consider, for various families of discrete random matrices. the probability that a random matrix A is surjective as a map A : Z m → Z n. In particular we show that, for a fairly robust family of random matrices, the probability that A : Z (2+epsilon)n→ Z n is surjective converges to 1. We then show that if we weaken the conditions on this family, we can produce counterexamples of large matrices with low probability of being surjective.
520 $a We also show that under "ideal" circumstances (that is, when the matrices are uniformly distributed in Z&d14; ), the probability that a matrix is surjective is neatly described by CohenLenstra heuristics (interestingly, the same heuristics that are conjectured to govern the behavior of class groups of random number fields).
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Yale University. $3 1178968
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10631631 $z click for full text (PQDT)

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