Random Discrete Structures / Edition 1

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Overview

The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for mathematicians and students.
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Product Details

Table of Contents

Foreword
Preface
Probability distributions on cladograms 1
Stability of self-organizing processes 19
Some examples of normal approximations by Stein's method 25
Large deviations for random distribution of mass 45
Random minimax game tress 55
Metrics on compositions and coincidences among renewal sequences 81
The no long odd cycle theorem for completely positive matrices 103
A note on triangle-free graphs 117
Intersections and limits of regenerative sets 121
Random processes of the form [actual symbol not reproducible] (mod p) where b[subscript n] takes on a single value 153
The second moment method, conditioning and approximation 175
How fast and where does a random walker move on a random tree? 185
A note on recurrence, amenability, and the universal cover of graphs 199
On which graphs are all random walks in random environments transient? 207
Energy, and intersections of Markov chains 213
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