Extremal Segments in Random Sequences

Details Extremal Segments in Random Sequences Extremal Segments in Random Sequences

1994-08-29

arxiv.org/abs/cond-mat/9408091v2

J. Phys. A27 (Letter to Editor), L907-L911 (1994)

Physics

Condensed Matter

3 pages, REVTEX 3.0, with multicol.sty, epsf.sty and EPS figures appended via uufiles. (Email in case of trouble.) CHANGES: Mi

Scientific paper

10.1088/0305-4470/27/24/001

We investigate the probability for the largest segment in with total displacement $Q$ in an $N$-step random walk to have length $L$. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large $N$ limit. In particular, the size of the longest loop has a distribution with a square-root singularity at $\ell\equiv L/N=1$, an essential singularity at $\ell=0$, and a discontinuous derivative at $\ell=1/2$.

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