Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Abstract
Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW 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 neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.
Cite
@article{arxiv.cond-mat/9507005,
title = {Randomly Charged Polymers, Random Walks, and Their Extremal Properties},
author = {Deniz Ertas and Yacov Kantor},
journal= {arXiv preprint arXiv:cond-mat/9507005},
year = {2009}
}
Comments
33 pages, 19 Postscript figures, RevTeX