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

The measurable space (S^',S^') into which a random variable from a probability space is a measurable function.

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

In random number computation, a seed is an initial number used as the starting point in a random number generating algorithm. In a dynamical system, a seed is a starting ...

Stochastic optimization refers to the minimization (or maximization) of a function in the presence of randomness in the optimization process. The randomness may be present as ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...