Studies on Extremal Segments in Random Sequences

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Turkish Journal of Physics
Volume:23 Issue:1
Studies on Extremal Segments in Random Sequences

Studies on Extremal Segments in Random Sequences

Authors : Deniz ERTAŞ

Pages : 105-112

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We review our main findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers. Upon mapping to one--dimensional random walks insert ignore into journalissuearticles values(RWs);, this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. 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 \ell\equiv L/N = 1, an essential singularity at \ell = 0, and a discontinuous derivative at \ell = 1/2.
Keywords : Turk J Phys, 23, 1999, 105 112 Turk J Phys, vol 23, iss 1

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