The canonical way to establish the central limit theorem for i.i.d. random variables is to use
characteristic functions and Lévy'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.
