Related papers: Dixie cup problem in an interlacing process
Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \cite{PolyaUrn}, starting from a particular type of recurrence differential equation it is used an analytic approach to recover…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher dimensions. Roughly speaking, in the one-dimensional setting,…
We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…
We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…
In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller's characterization of discrete infinitely divisible distributions to signed discrete…
Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the…
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a…
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
We consider predictions of the random number and the magnitude of each iid component in a random sum based on its distributional structure, where only a total value of the sum is available and where iid random components are non-negative.…
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…
This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled…
Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…