TY  - BOOK
AU  - Féray,Valentin
AU  - Méliot,Pierre-Loïc
AU  - Nikeghbali,Ashkan
ED  - SpringerLink (Online service)
TI  - Mod-ϕ Convergence: Normality Zones and Precise Deviations 
T2  - SpringerBriefs in Probability and Mathematical Statistics,
SN  - 9783319468228
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Distribution (Probability theory
KW  - Number theory
KW  - Combinatorics
KW  - Matrix theory
KW  - Probability Theory and Stochastic Processes
KW  - Number Theory
KW  - Linear and Multilinear Algebras, Matrix Theory
N1  - Preface -- Introduction -- Preliminaries -- Fluctuations in the case of lattice distributions -- Fluctuations in the non-lattice case -- An extended deviation result from bounds on cumulants -- A precise version of the Ellis-Gärtner theorem -- Examples with an explicit generating function -- Mod-Gaussian convergence from a factorisation of the PGF -- Dependency graphs and mod-Gaussian convergence -- Subgraph count statistics in Erdös-Rényi random graphs -- Random character values from central measures on partitions -- Bibliography
N2  - 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-ϕ 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.
UR  - https://doi.org/10.1007/978-3-319-46822-8
ER  -