Related papers: The number of distinct adjacent pairs in geometric…
A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for…
Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the r-th left-to-right maximum, for fixed r and large n.
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the r-th left-to-right maximum counted from the right, for fixed r and n->oo. This complements previous…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
For words of length $n$, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, $q$--analogues for these…
In this work we explore the dissimilarity between symmetric word pairs, by comparing the inter-word distance distribution of a word to that of its reversed complement. We propose a new measure of dissimilarity between such distributions.…
We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
In $M$-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric…
Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…