This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various

We prove the existence of, and describe, a (random) process which builds subtrees of a rooted d-branching tree one node at a time, in such a way that the subtree created at stage n is precisely a uniformly random subtree of size n. The union of these subtrees is a "uniformly random &

This paper presents some first results on how to perform uniform random walks (where every trace has the same probability to occur) in very large models. The models considered here are described in a succinct way as a set of communicating reactive modules. The method relies upon techniques

A uniform random intersection graph G(n, m, k) is a random graph constructed as follows. Label each of n nodes by a randomly chosen set of k distinct colours taken from some finite set of possible colours of size m. Nodes are joined by an edge if and only if some colour appears in both their labels

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. We also present some new results concerning the moments of uniform random walks, in particular their derivatives. 1

Controlled non uniform random generation of decomposable structures

are unbiased. The exception is some bias near concave features of the boundary to ensure well-shaped cells. The method is extensible to generating Voronoi cells that agree on both sides of two-sided internal boundaries. Maximal uniform sampling leads naturally to bounds on the aspect ratio and dihedral angles

The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floating-point arithmetic. The resulting ADZ method enables one to generate decomposable data structures --- both labelled or unlabelled --- uniformly

In an earlier report [1] we described methods to obtain pseudorandom numbers from various statistical distributions as well as more general methods. The underlying generators giving uniformly distributed random number between zero and one was only briefly described. In this report we try

in terms of prime components and, by studying the tilings with respect to the length of the strip and to the number of prime components, we are able to give an algorithm which uniformly generate a random tiling of length n in time O(n), where the constant multiplying n is strictly less then 1.