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  2. Free probability - Wikipedia

    en.wikipedia.org/wiki/Free_probability

    The relation of free probability with random matrices is a key reason for the wide use of free probability in other subjects. Voiculescu introduced the concept of freeness around 1983 in an operator algebraic context; at the beginning there was no relation at all with random matrices.

  3. Random matrix - Wikipedia

    en.wikipedia.org/wiki/Random_matrix

    The relation of free probability with random matrices [22] is a key reason for the wide use of free probability in other subjects. Voiculescu introduced the concept of freeness around 1983 in an operator algebraic context; at the beginning there was no relation at all with random matrices.

  4. Stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Stochastic_matrix

    A substochastic matrix is a real square matrix whose row sums are all ; In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a probability vector.

  5. Free convolution - Wikipedia

    en.wikipedia.org/wiki/Free_convolution

    Free convolution is the free probability analog of the classical notion of convolution of probability measures. Due to the non-commutative nature of free probability theory, one has to talk separately about additive and multiplicative free convolution, which arise from addition and multiplication of free random variables (see below; in the classical case, what would be the analog of free ...

  6. Wigner semicircle distribution - Wikipedia

    en.wikipedia.org/wiki/Wigner_semicircle_distribution

    In free probability theory, the role of Wigner's semicircle distribution is analogous to that of the normal distribution in classical probability theory. Namely, in free probability theory, the role of cumulants is occupied by "free cumulants", whose relation to ordinary cumulants is simply that the role of the set of all partitions of a finite ...

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  8. Algebra of random variables - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_random_variables

    The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis. One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.

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