Probability theory has grown from a modest study of simple games of change to a subject with application in almost every branch of knowledge and science. In this exciting book, a number of distinguished probabilists discuss their current work and applications in an easily understood manner. Chapters show that new directions in probability have been suggested by the application of probability to other fields and other disciplines of mathematics. The study of polymer chains in chemistry led to the study of self-avoiding random walks; the study of the Ising model in physics and models for epidemics in biology led to the study of the probability theory of interacting particle systems. The stochastic calculus has allowed probabilists to solve problems in classical analysis, in theory of investment, and in engineering. The mathematical formulation of game theory has led to new insights into decisions under uncertainty. These new developments in probability are vividly illustrated throughout the book.
Uniform Random Spanning Trees. Random Walks: Simple and Self Avoiding. Some Connections between Brownian Motion and Analysis via Stochastic Calculus. Can You Feel the Shape of a Manifold with Brownian Motion? Some New Games for Your Computer. Cellular Automata with Errors: Problems for Students of Probability. Metropolis-Type Monte Carlo Simulation Algorithms and Simulated Annealing. Random Graphs in Ecology. How Many Times Should You Shuffle a Deck of Cards? Stochastic Games and Operators. "Decisions, Decisions": The Bandit Model for Decision Processes, Optimal Strategy, and Computer Implementation. Three Bewitching Paradoxes. Index.