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PROBABILISTIC DIVIDE-AND-CONQUER { A NEW METHOD FOR
EXACT SIMULATION { AND LOWER BOUND EXPANSIONS FOR
RANDOM BERNOULLI MATRICES VIA NOVEL INTEGER PARTITIONS
by
Stephen Anthony DeSalvo
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
May 2012
Copyright 2012 Stephen Anthony DeSalvo
Object Description
| Title | Probabilistic divide-and-conquer -- a new method of exact simulation -- and lower bound expansions for random Bernoulli matrices via novel integer partitions |
| Author | DeSalvo, Stephen Anthony |
| Author email | sdesalvo@usc.edu;stephendesalvo@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2012-02-22 |
| Date submitted | 2012-05-03 |
| Date approved | 2012-05-03 |
| Restricted until | 2012-05-03 |
| Date published | 2012-05-03 |
| Advisor (committee chair) | Arratia, Richard |
| Advisor (committee member) |
Goldstein, Larry Ross, Sheldon |
| Abstract | This thesis is divided into two areas of combinatorial probability: probabilistic divide-and-conquer, and random Bernoulli matrices via novel integer partitions. ❧ Probabilistic divide-and-conquer is a new method of exact sampling that simulates from a set of objects by dividing each object into two disjoint parts, and pieces them together. ❧ The study of random Bernoulli matrices is driven by the asymptotics of the probability that a random matrix whose entries are independent, identically distributed Bernoulli random variables with parameter 1/2 is singular. Our approach is an inclusion-exclusion expansion for this probability, defining a necessary and sufficient class of integer partitions as an index set to characterize all of the singularities. |
| Keyword | integer partitions; probability; random sampling; combinatorial structures; Sperner's lemma; random Bernoulli matrices; lower bound expansions; inclusion-exclusion; Bernoulli orthogonal complement; asymptotic expansion; Bayes' theorem; confidence interval; grand canonical ensemble |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | DeSalvo, Stephen Anthony |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume4/etd-DeSalvoSte-737-0.pdf |
Description
| Title | Page 1 |
| Full text | PROBABILISTIC DIVIDE-AND-CONQUER { A NEW METHOD FOR EXACT SIMULATION { AND LOWER BOUND EXPANSIONS FOR RANDOM BERNOULLI MATRICES VIA NOVEL INTEGER PARTITIONS by Stephen Anthony DeSalvo A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) May 2012 Copyright 2012 Stephen Anthony DeSalvo |
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