Related papers: Approximation Theorems Related to the Coupon Colle…
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…
We study how efficiently a $k$-element set $S\subseteq[n]$ can be learned from a uniform superposition $|S\rangle$ of its elements. One can think of $|S\rangle=\sum_{i\in S}|i\rangle/\sqrt{|S|}$ as the quantum version of a uniformly random…
Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…
A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension $d$ that have sample complexity $\Omega\left(\frac…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
We study the two-player coupon-collector competition in which two independent collectors draw one coupon each per round from a set of $d$ equally likely coupon types. Myers and Wilf gave finite formulae for several two-player events and…
We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given…
To reduce computational complexity and delay in randomized network coded content distribution (and for some other practical reasons), coding is not performed simultaneously over all content blocks but over much smaller subsets known as…
Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…
Let $X_1,\ldots,X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density $f$. Under some conditions on $f$, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability…
Computer-based tests with randomly generated questions allow a large number of different tests to be generated. Given a fixed number of alternatives for each question, the number of tests that need to be generated before all possible…
The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning…
We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential…
The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no…
Consider n items located randomly on a circle of length 1. The locations of the items are assumed to be independent and uniformly distributed on [0,1). A picker starts at point 0 and has to collect all n items by moving along the circle at…