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Correlations on the strata of a random mapping
Author(s) -
Drmota Michael
Publication year - 1995
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.3240060223
Subject(s) - independent and identically distributed random variables , mathematics , combinatorics , limit (mathematics) , singularity , central limit theorem , multivariate statistics , random variable , joint probability distribution , discrete mathematics , mathematical analysis , statistics
Mutafchiev [7] observed that μ n (k) the number of points in random mappings on {1,…, n} with distance k to cyclic points is asymptotically identically distributed with the number of cyclic points μ n (0) if k = o (√n) by using the fact that (μ n (k) ‐ μ n (0))√n 0 in probability. The main purpose of this paper is to provide a local limit theorem for the joint distribution of μ n (k 1 ), μ n (k 2 ). Furthermore, we prove a local version of Mutafchiev's result. All results are obtained by applying singularity analysis of multivariate generating functions.