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Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. In 1921, Pólya proved that p(1)=p(2)=1, (1) but p(d)<1 (2) for d>2. Watson (1939), ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

A shuffling algorithm used in a class of random number generators.

A random polygon containing the origin (Kovalenko 1999).

A slightly archaic term for a computer-generated random number. The prefix pseudo- is used to distinguish this type of number from a "truly" random number generated by a ...

A lottery in which three numbers are picked at random from the integers 1-14.

Random walk trajectories which are composed of self-similar jumps. They are described by the Lévy distribution.

Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable X with a probability density ...