Large Deviations Techniques and Applications (Applications of Mathematics, 38)

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Summary: Dembo and Zeitouni on Large Deviations
Review: This is the definitive book in the new mushrooming mathematical field of large deviations, which everybody should know including mathematicians, physical scientists, social and behavioral scientists, life scientists, etc. Large deviations refers to rare and extreme events, which are studied by examining the extreme ends or "tails" of graphs (which is where graphs usually get narrower and narrower). My own research is also largely in the field of rare events, but I study them more directly by using logic-based probability, defined as the probability of the set/event analogue of the logical conditional A-->B = A' U B (see abstracts of about 35 of my papers at the Institute for Logic of the University of Vienna, available on the internet). Dembo and Zeitouni study rare events by more standard methods, but the results make fascinating reading and give ideas for all kinds of research. This type of research differs from the usual preoccupation of scientists with common events, frequent events, average events, and so. It has become obvious that the rare events, such as great genius, great discoveries and creativity, accidental events, catastrophes, and so on, play an extremely important role in the world. Dembo and Zeitouni are examples of the best in Israeli research, although they have never responded to my inquiries (perhaps they are too busy being great geniuses).