Abstract
With a given transformation on a finite domain, we associate a three-dimensional distribution function describing the component size, cycle length and trajectory length of each point in the domain.We then consider a random transformation on the domain, in which images of points are independent and identically distributed. The three-dimensional distribution function associated with this random transformation is itself random. We show that, under a simple homogeneity condition on the distribution of images, and with a suitable scaling, this random distribution function has a limit law as the number of points in the domain tends to
Citation
C. A. O'Cinneide. A. V. Pokrovskii. "Nonuniform random transformations." Ann. Appl. Probab. 10 (4) 1151 - 1181, November 2000. https://doi.org/10.1214/aoap/1019487611
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