Dynamics on Graphs

Auteur
Rick Durrett is James B. Duke Emeritus Professor of Mathematics at Duke University. He received his Ph.D. in Operations Research from Stanford University in 1976. After nine years at the University of California, Los Angeles and twenty-five at Cornell University, he moved to Duke University in 2010, where he worked until he retired in 2023. Durrett is the author of eight books and more than 240 journal articles on a wide variety of topics in probability theory and its applications to ecology, genetics, cancer, and epidemiology. He has supervised fifty-one Ph.D. students. He has been a member of the National Academy of Sciences since 2007.

Texte du rabat

This extensive revision of the 2007 book 'Random Graph Dynamics,' covering the current state of mathematical research in the field, is ideal for researchers and graduate students. It considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs. However, it investigates a wide variety of dynamics. The author describes results for the 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. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

Contenu

Preface; Notation; 1. Erd s-Renyi random graphs; 2. General degree distributions; 3. Inhomogeneous random graphs; 4. Epidemics; 5. Contact process; 6. Random walks, mixing times; 7. Voter models, coalescing RWs; 8. Coevolving systems; Appendix. Large deviations; Books and Long Surveys; Index.