Extremal Segments in Random Sequences

Abstract

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 $\ell =1/2$.

3 pages, REVTEX 3.0, with multicol.sty, epsf.sty and EPS figures appended via uufiles. (Email in case of trouble.) CHANGES: Missing figure added to figures.uu MIT-CMT-KE-94-1

References in corpus (1)

• Instabilities of Charged Polyampholytes

Cited by in corpus (7)

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• A Model Ground State of Polyampholytes
• THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT
• Statistics of Largest Loops in a Random Walk