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In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

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 ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...

A marked point process with mark space E is a double sequence (T,Y)=((T_n)_(n>=1),(Y_n)_(n>=1)) of R^^^+-valued random variables and E^_-valued random variables Y_n defined ...

A sequence of random variates X_0, X_1, ... with finite means such that the conditional expectation of X_(n+1) given X_0, X_1, X_2, ..., X_n is equal to X_n, i.e., ...

A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

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) ...

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 ...

A simple point process (or SPP) is an almost surely increasing sequence of strictly positive, possibly infinite random variables which are strictly increasing as long as they ...