Related papers: Limit distributions for the problem of collecting …
We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…
In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…
We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.
We compute the limiting distribution, as n approaches infinity, of the number of cycles of length between gamma n and delta n in a permutation of [n] chosen uniformly at random, for constants gamma, delta such that 1/(k+1) <= gamma < delta…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
A collector samples coupons with replacement from a pool containing $g$ \textit{uniform} groups of coupons, where "uniform group" means that all coupons in the group are equally likely to occur. For each $j = 1, \dots, g$ let $T_j$ be the…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies…
We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We…
A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as…
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
What is the smallest number of random transpositions (meaning that we swap given pairs of elements with given probabilities) that we can make on an $n$-point set to ensure that each element is uniformly distributed -- in the sense that the…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we…
We study the local limit distribution of the number of occurrences of a symbol in words of length $n$ generated at random in a regular language according to a rational stochastic model. We present an analysis of the main local limits when…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…