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Extremal Properties of Random Systems

L. Frachebourg·I. Ispolatov·P. L. Krapivsky
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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 $k=2,3,\ldots$ 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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L. Frachebourg, I. Ispolatov, P. L. Krapivsky. 1995-07-05. Extremal Properties of Random Systems. https://doi.org/10.1103/physreve.52.r5727

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