Loops in one-dimensional random walks |
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Authors: | S Wolfling Y Kantor |
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Institution: | (1) School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel, IL |
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Abstract: | Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive
and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate numerically
and analytically loops in several types of RWs, including RWs with continuous step-length distribution. We show that for long
walks the probability density of the longest loop becomes independent of the details of the walks and definition of the loops.
We investigate crossovers and convergence of probability densities to the limiting behavior, and obtain some of the analytical
properties of the universal probability density.
Received 8 January 1999 |
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Keywords: | PACS 02 50 -r Probability theory stochastic processes and statistics – 05 40 -a Fluctuation phenomena random processes noise and Brownian motion – 36 20 -r Macromolecules and polymer molecules |
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