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,… which become weaker and weaker as k ∞; additionally, p(l) has an essential singularity at l=0. These properties are found also in many dimensional situation.
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