Extremal Properties of Random Systems

Abstract

We find that the probability distribution for the largest intervals $p(l)$ exhibits universal properties for different systems including random walk and random cutting models. In particular, $p(l)$ has an infinite set of singularities at $l=1/k$ with $k=2,3,\dots$ which become weaker and weaker as $k\to \infty$; additionally, $p(l)$ has an essential singularity at $l=0$. These properties are found also in many dimensional situation.

4 pages, uuencoded PostScript file with 3 figures included

References in corpus (1)

• Extremal Segments in Random Sequences

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