Extremal Properties of Random Systems

Details Extremal Properties of Random Systems Extremal Properties of Random Systems

1995-07-05

arxiv.org/abs/cond-mat/9507009v1

Physics

Condensed Matter

4 pages, uuencoded PostScript file with 3 figures included

Scientific paper

10.1103/PhysRevE.52.R5727

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 $k=2,3,\ldots$ 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.

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