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The canonical way to establish the central limit theorem for i.i.d.
random variables is to use characteristic functions and Levy's
continuity theorem. This monograph focuses on this characteristic
function approach and presents a renormalization theory called mod-
convergence. This type of convergence is a relatively new concept
with many deep ramifications, and has not previously been published
in a single accessible volume. The authors construct an extremely
flexible framework using this concept in order to study limit
theorems and large deviations for a number of probabilistic models
related to classical probability, combinatorics, non-commutative
random variables, as well as geometric and number-theoretical
objects. Intended for researchers in probability theory, the text
is carefully well-written and well-structured, containing a great
amount of detail and interesting examples.
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