The theory of large deviations deals with rates at which
probabilities of certain events decay as a natural parameter in the
problem varies. This book, which is based on a graduate course on
large deviations at the Courant Institute, focuses on three
concrete sets of examples: (i) diffusions with small noise and the
exit problem, (ii) large time behavior of Markov processes and
their connection to the Feynman-Kac formula and the related large
deviation behavior of the number of distinct sites visited by a
random walk, and (iii) interacting particle systems, their scaling
limits, and large deviations from their expected limits. For the
most part the examples are worked out in detail, and in the process
the subject of large deviations is developed. The book will give
the reader a flavor of how large deviation theory can help in
problems that are not posed directly in terms of large deviations.
The reader is assumed to have some familiarity with probability,
Markov processes, and interacting particle systems.
General
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