We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNGs) that use wholly deterministic algorit...

From security to randomized algorithms, there are many existing problems whose solutions are fundamentally based on the assumption that intrinsically pure random number sources exist. Pseudorandom number generators can imitate randomness sufficiently well for most applications, however, they still rely on some secret seed input. Hardware random number generators attempt to extract randomness di...

The increasing popularity and complexity of random number intensive methods such as simulation and bootstrapping in econometrics requires researchers to have a good grasp of random number generation in general, and the specific generators that they employ in particular. Here, we discuss the random number generation options, their specifications, and their implementations in gretl. We also asses...

The generation of continuous random variables on a digital computer encounters a problem of accuracy caused by approximations and discretization error. These in turn impose a bias on the simulation results. An ideal discrete approximation of a continuous distribution and a measure of error are proposed. Heuristic analysis of common methods for transforming uniform deviates to other continuous r...

Classical floating point random numbers fail simple tests when considered as rational numbers. A uniform random number generator based on a linear congruential generator with output in the rational numbers is implemented within the two computer algebra systems Maple 10 and MuPAD Pro 3.1. The empirical tests in Knuth’s suite of tests show no evidence against the hypothesis that the output sample...

We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive single photon detections is used to generate random bit. In experiment, von Neumann correction method is applied to extract the final random bit. This method is...

Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide “true” random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers (Xn)n as independent uniform samples in a range 0, . . . 2 − 1, with b = 8, 16, 32 or b = 64. In applications, it is instead sometimes desirabl...

In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies critically on the independence of the source, a notion we rigorously define for our model. In real cases, affected by imperfections in measurement and hardware...

Due to imperfections in measurement and hardware, the flow of bits generated by a quantum random number generator (QRNG) contains bias and correlation, two symptoms of non-randomness. There is no algorithmic method to eliminate correlation as this amounts to guaranteeing incomputability. However, bias can be mitigated: QRNGs use normalisation techniques such as von Neumann’s method—the first an...

In this paper we discuss major problems related to reliability of random number generators used for simulation studies. We propose the decimals of π as the most reliable random number generator as compared to certain real normal numbers as well as all families of pseudorandom number generators. A new property that a random number generator must have is introduced. Two applications are discussed.