Functional central limit theorems in L(0, 1) for logarithmic combinatorial assemblies
نویسنده
چکیده
Functional central limit theorems in L(0, 1) for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in L(0, 1) whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized random processes which converge weakly to a corresponding Gaussian process with additional assumptions.
منابع مشابه
Strong convergence on weakly logarithmic combinatorial assemblies
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the author’s analytic approach, we generalize the so-called Fundamental Lemma giving independent process approximation in the total variation distance of the compone...
متن کاملLimit shapes of multiplicative measures associated with coagulation-fragmentation processes and random combinatorial structures
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak ∼ Ck, k → ∞, p > 0, where C is a positive constant. The measures considered are associated with reversible coagulationfragmentation processes and combinatorial structures, known as assemblies. We prove a functional central limit theorem...
متن کاملBerry–esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences, Using Zero and Size Biasing
Berry–Esseen-type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are a...
متن کاملSelf-normalized limit theorems: A survey
Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...
متن کاملOn Poisson-Dirichlet limits for random decomposable combinatorial structures
We prove a joint local limit law for the distribution of the r largest components of decomposable logarithmic combinatorial structures, including assemblies, multisets and selections. Our method is entirely probabilistic, and requires only weak conditions that may readily be verified in practice. Combinatorics, Probability and Computing (1999) 8, 193–208. Printed in the United Kingdom c © 1999 ...
متن کامل