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FROM CARD SHUFFLING TO RANDOM WALKS ON CHAMBERS OF
HYPERPLANE ARRANGEMENTS
by
Meghdi Aboulian
A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(APPLIED MATHEMATICS)
May 2010
Copyright 2010 Meghdi Aboulian
Object Description
| Title | From card shuffling to random walks on chambers of hyperplane arrangements |
| Author | Aboulian, Meghdi |
| Author email | maboulia@usc.edu; meghedi_a4@yahoo.com |
| Degree | Master of Science |
| Document type | Thesis |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2010-03-24 |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-04-14 |
| Advisor (committee chair) | Fulman, Jason |
| Advisor (committee member) |
Alexander, Kenneth Ross, Sheldon |
| Abstract | I have surveyed basic properties of card shuffling techniques as well as generalized theory of random walks on chambers of hyperplane arrangements based on the works of P. Diaconis and his coauthors. Chapter one starts with examples of shuffling techniques and gives their distributions as probability measures on symmetric group. Main theorems proven in chapter one give estimates of total variation distance as a measure of required number of shuffles. Chapter two contains definition of random walk on chambers of hyperplane arrangements and proves theorems about upper bounds for total variation distance. |
| Keyword | card shuffling; random walk; total variance distance; riffle shuffling; top to random shuffling; random walks on chambers of hyperplane arrangements; stationary distribution; applications to card shuffling; card shuffling techniques |
| 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-m2909 |
| Rights | Aboulian, Meghdi |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-ABOULIAN-3595 |
| Archival file | uscthesesreloadpub_Volume48/etd-ABOULIAN-3595.pdf |
Description
| Title | Page 1 |
| Full text | FROM CARD SHUFFLING TO RANDOM WALKS ON CHAMBERS OF HYPERPLANE ARRANGEMENTS by Meghdi Aboulian A Thesis Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (APPLIED MATHEMATICS) May 2010 Copyright 2010 Meghdi Aboulian |
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