Random Numbers

  Random numbers are particular occurrences of random variables. They are used in Monte Carlo calculations, where three different types may be distinguished according to the method used to generate them:

• a) Truly random numbers are unpredictable in advance and can only be generated by a physical process such as radioactive decay: in the presence of radiation, a Geiger counter will record particles at time intervals that follow a truly random (exponential) distribution.
• b) Pseudorandom numbers are those most often used in Monte Carlo calculations. They are generated by a numerical algorithm, and are therefore predictable in principle, but appear to be truly random to someone who does not know the algorithm.
• c) Quasirandom numbers are also generated by a numerical algorithm, but are not intended to appear to have the properties of a truly random sequence, rather they are optimized to give the fastest convergence of the Monte Carlo calculation.