Related papers: Random variate generation using only finitely many…
In 1952, von Neumann introduced the rejection method for random variate generation. We revisit this algorithm when we have a source of perfect bits at our disposal. In this random bit model, there are universal lower bounds for generating a…
In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Consider $n$ independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a *head* and a *tail*, or flipped all…
In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
This article studies the fundamental problem of using i.i.d. coin tosses from an entropy source to efficiently generate random variables $X_i \sim P_i$ $(i \ge 1)$, where $(P_1, P_2, \dots)$ is a random sequence of rational discrete…
We describe a methodology and standard of proof for experimental claims of quantum random number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations,…
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
Let $q \in (0,1)$ and $\delta \in (0,1)$ be real numbers, and let $C$ be a coin that comes up heads with an unknown probability $p$, such that $p \neq q$. We present an algorithm that, on input $C$, $q$, and $\delta$, decides, with…
This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…