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Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

A random process whose future probabilities are determined by its most recent values. A stochastic process x(t) is called Markov if for every n and t_1<t_2...<t_n, we have ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

A spatial-temporal point process is a point process which models data that is localized at a discrete set of locations in both space and time. In particular, a ...

The voter model is a simple mathematical model of opinion formation in which voters are located at the nodes of a network, each voter has an opinion (in the simplest case, 0 ...