Dissertation/Thesis Abstract

From card shuffling to random walks on chambers of hyperplane arrangements
by Aboulian, Meghdi, M.S., University of Southern California, 2010, 55; 1476256
Abstract (Summary)

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.

Indexing (document details)
Advisor: Fulman, Jason
Commitee: Alexander, Kenneth, Ross, Sheldon
School: University of Southern California
Department: Applied Mathematics
School Location: United States -- California
Source: MAI 48/05M, Masters Abstracts International
Subjects: Applied Mathematics
Keywords: Card shuffling, Random walks, Riffle shuffling, Stationary distribution, Top to random shuffling, Total variance distance estimate
Publication Number: 1476256
ISBN: 978-1-109-77439-9
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