TY - JOUR
T1 - Extremal segments in random sequences
AU - Kantor, Y.
AU - Ertas, D.
PY - 1994
Y1 - 1994
N2 - We investigate the probability for the largest segment 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 square-root singularity at l identical to L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2.
AB - We investigate the probability for the largest segment 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 square-root singularity at l identical to L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2.
UR - http://www.scopus.com/inward/record.url?scp=21844497217&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/27/24/001
DO - 10.1088/0305-4470/27/24/001
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AN - SCOPUS:21844497217
SN - 0305-4470
VL - 27
SP - L907-L911
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 24
M1 - 001
ER -