This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling methods, Poisson approximation (the Stein-Chen method), concentration inequalities (Chernoff bounds and Azuma-Hoeffding inequality) and branching processes. The authors examine the small-world phenomenon, preferential attachment, as well as classical epidemics. --from publisher description.
Series Statement
London Mathematical Society lecture note series ; 369
Uniform Title
London Mathematical Society lecture note series 369.
Includes bibliographical references (p. [117]-121) and index.
Processing Action (note)
committed to retain
Contents
Galton-Watson branching processes -- Reed-Frost epidemics and Erdős-Rényi random graphs -- Connectivity and Poisson approximation -- Diameter of Erdős-Rényi graphs -- From microscopic to macroscopic dynamics -- The small-world phenomenon -- Power laws via preferential attachment -- Epidemics on general graphs -- Viral marketing and optimised epidemics.