chapter  2
50 Pages

Generating Random Numbers

Stochastic simulations and especially the Monte Carlo method use random variables (RVs). So the ability to provide random numbers (RNs) with a specified distribution becomes necessary. The main problem is to find numbers that are really random and unpredictable. Of course, throwing dice is much too slow for most applications as usually a lot of RNs are needed. An alternative is to use physical phenomena like radioactive decay, which is often considered as a synonym for randomness, and then to transformmeasurements into RNs. With the right equipment this works much faster. But how can one ensure that the required distribution is mimicked? Indeed, modern research makes it possible to use physical devices for random number generation by transforming the measurements so that they deliver a good approximation to a fixed distribution, but those devices still are too slow for extensive simulations. Another disadvantage is that the sequence of RNs cannot be reproduced unless they have been stored. Reproducibility is an important feature for Monte Carlo methods, e.g. for variance reduction techniques, or simply for debugging reasons. However, physical random number generators (RNGs) are useful for applications in cryptography or gambling machines, when you have to make sure that the numbers are absolutely unpredictable.