Related papers: A Central Limit Theorem for Repeating Patterns
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Let $(X_i)_{i \geq 1}$ and $(Y_i)_{i\geq1}$ be two independent sequences of independent identically distributed random variables taking their values in a common finite alphabet and having the same law. Let $LC_n$ be the length of the…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…
We compute the limit distribution for (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by…
Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…
We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of…
We consider the distribution of the length of the longest subsequence avoiding a given pattern in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to avoiding the pattern 21. We show…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
The purpose of this work is to establish a central limit theorem that can be applied to a particular form of Markov chains, including the number of descents in a random permutation of $\mathfrak{S}_n$, two-type generalized P{\'o}lya urns,…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of $n$ independent observations from a continuous distribution $F$, and we prove a central limit theorem for the number of selections…
We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.
The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a fixed conjugacy class of the symmetric group. Our technique…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…