相关论文: A generalization of the Birthday problem and the c…
We motivate and prove a version of the birthday paradox for $k$ identical bosons in $n$ possible modes. If the bosons are in the uniform mixed state, also called the maximally mixed quantum state, then we need $k \sim \sqrt{n}$ bosons to…
As an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete…
This article brings forward an estimation of the proportion of homonyms in large scale groups based on the distribution of first names and last names in a subset of these groups. The estimation is based on the generalization of the…
We give an elementary statistical analysis of two High Performance Computing issues, processor cache mapping and network port mapping. In both cases we find that, as in the birthday paradox, random assignment leads to more frequent…
The assumption of fingerprint uniqueness is foundational in forensic science and central to criminal identification practices. However, empirical evidence supporting this assumption is limited, and recent findings from artificial…
We prove a Kolmogorov complexity variant of the birthday paradox. Sufficiently sized random subsets of strings are guaranteed to have two members x and y with low K(x/y). To prove this, we first show that the minimum conditional Kolmogorov…
A birthday surprise is the event that, given k uniformly random samples from a sample space of size n, at least two of them are identical. We show that Bernoulli numbers can be used to derive arbitrarily exact bounds on the probability of a…
We introduce a fun problem that can be considered as a variant of the classic birthday problem, the Bottleneck Birthday Problem (BBP). It is stated as: what is the maximum number of people we have to choose so that no day of the year has…
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…
We study a birthday inequality in random geometric graphs: the probability of the empty graph is upper bounded by the product of the probabilities that each edge is absent. We show the birthday inequality holds at low densities, but does…
What is the chance that among a group of $n$ friends, there are $s$ friends all of whom have the same birthday? This is the celebrated birthday problem which can be formulated as the existence of a monochromatic $s$-clique $K_s$…
Birthday problem is a well-known classic problem in probability theory widely applied in cryptography, and bubble sort is a popular sorting algorithm leading to some interesting theoretical problems in computer science. However, the…
Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at…
This article, based on a talk, treats some elementary, but not completely simple examples from probability. They concern multiple birthday coincidences, throwing dice, the combinatorics of the German card game "Doppelkopf", and the…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
Surreal numbers are created recursively, with the "birthday" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday…
A strategy for playing the game of roulette is presented in this paper. The strategy is based on the same probabilistic argument that leads to the well-known Birthday Paradox in Probability theory. Following the strategy, a player will have…
Let $T(H, G_n)$ be the number of monochromatic copies of a fixed connected graph $H$ in a uniformly random coloring of the vertices of the graph $G_n$. In this paper we give a complete characterization of the limiting distribution of $T(H,…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Our question is ``What is the probability that at least three members of the senate share the same birthday?'' Before the pandemic, I asked this question in several popular math talks I gave at universities across the country. Inspired by…