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Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures
Author(s) -
Mutafchiev Lyuben R.
Publication year - 1992
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.3240030405
Subject(s) - mathematics , limit (mathematics) , series (stratigraphy) , central limit theorem , exponential function , random graph , combinatorics , discrete mathematics , random variable , convergence (economics) , convergence of random variables , power series , statistics , mathematical analysis , graph , paleontology , economics , biology , economic growth
A Local limit theorem for the distribution of the number of components in random labelled relational structures of size n (e.g., a type of random graphs on n vertices, random permutations of n elements, etc.) is proved as n →∞. The case when the corresponding exponential generating functions diverge at their radii of convergence is considered.