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010   $a3-319-46822-7
024 7 $a10.1007/978-3-319-46822-8
035   $a(CKB)4340000000024208
035   $a(DE-He213)978-3-319-46822-8
035   $a(MiAaPQ)EBC4765262
035   $a(PPN)197453961
035   $a(EXLCZ)994340000000024208
100   $a20161206d2016      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aMod-? convergence $enormality zones and precise deviations /$fby Valentin Féray, Pierre-Loďc Méliot, Ashkan Nikeghbali
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XII, 152 p. 17 illus., 9 illus. in color.)
225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333
311   $a3-319-46821-9 
320   $aIncludes bibliographical references.
327   $aPreface -- 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.
330   $aThe canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy?s continuity theorem. This monograph focuses on this characteristic function approach and presents a renormalization theory called mod-? convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models related to classical probability, combinatorics, non-commutative random variables, as well as geometric and number-theoretical objects. Intended for researchers in probability theory, the text is carefully well-written and well-structured, containing a great amount of detail and interesting examples. .
410  0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333
606   $aProbabilities
606   $aNumber theory
606   $aCombinatorial analysis
606   $aMatrix theory
606   $aAlgebra
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
615  0$aProbabilities.
615  0$aNumber theory.
615  0$aCombinatorial analysis.
615  0$aMatrix theory.
615  0$aAlgebra.
615 14$aProbability Theory and Stochastic Processes.
615 24$aNumber Theory.
615 24$aCombinatorics.
615 24$aLinear and Multilinear Algebras, Matrix Theory.
676   $a519.2
700   $aFéray$b Valentin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755982
702   $aMéliot$b Pierre-Loďc$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aNikeghbali$b Ashkan$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910155277603321
996   $aMod-? Convergence$91964441
997   $aUNINA