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A Young tableau chosen at random from those having a given shape. A random tableau can be generated by RandomTableau[shape] in the Wolfram Language package Combinatorica` . ...

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) ...

A random variate is a variable generated from uniformly distributed pseudorandom numbers. Depending on how they are generated, a random variate can be uniformly or ...

A random walk is a sequence of discrete steps in which each step is randomly taken subject to some set of restrictions in allowed directions and step lengths. Random walks ...

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 ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

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. ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where ...

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...