Dynamics on Graphs
Description
This book is an extensive revision of the 2007 book Random Graph Dynamics . In contrast to the first edition, the new version considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs, but investigates a wide variety of dynamics. It describes results on convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Furthermore, Chapter 8 discusses a new, challenging, and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.
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Person
Rick Durrett received his Ph.D. in Operations Research from Stanford University in 1976. After nine years at UCLA, where he worked closely with Tom Liggett, he moved to Cornell to join a probability group with Harry Kesten, Frank Spitzer, and Eugene Dynkin. Twenty-five years and two children later, he moved to Duke, where he was a James B. Duke Professor of Mathematics until he retired on July 1, 2023. He is the author of eight books and more than 240 journal articles. He was elected a member of the National Academy of Sciences in 2007. During his career he has supervised 51 Ph.D. students, mentored three dozen postdocs, and introduced a large number of undergraduates to mathematical research through one-on-one mentoring and summer research programs.
Content
Chapter 1. Erdos-Renyi Random Graphs.- Chapter 2. General Degree Distributions.- Chapter 3. Inhomogeneous Random Graphs.- Chapter 4. Epidemics.- Chapter 5. Contact Process.- Chapter 6. Random Walks, Mixing Times.- Chapter 7. Voter Models, Coalescing RWs.- Chapter 8. Coevolving Systems.