caa a22 4500 469041811 CHVBK 20180323132813.0 cr unu---uuuuu 170328e19920501xx s 000 0 eng 10.1007/BF02847489 doi (NATIONALLICENCE)springer-10.1007/BF02847489 A myopic random walk on a finite chain [Elektronische Daten] [S Revathi, V Balakrishnan, M Valsakumar] We solve analytically the problem of a biased random walk on a finite chain of ‘sites' (1,2, ,N) in discrete time, with ‘myopic boundary conditions'—a walker at 1 (orN) at timen moves to 2 (orN − 1) with probability one at time (n + 1). The Markov chain has period two; there is no unique stationary distribution, and the moments of the displacement of the walker oscillate about certain mean values asn → ∞, with amplitudes proportional to 1/N. In the continuous-time limit, the oscillating behaviour of the probability distribution disappears, but the stationary distribution is depleted at the terminal sites owing to the boundary conditions. In the limit of continuous space as well, the problem becomes identical to that of diffusion on a line segment with the standard reflecting boundary conditions. The first passage time problem is also solved, and the differences between the walks with myopic and reflecting boundaries are brought out. Indian Academy of Sciences, 1992 Random walk nationallicence myopic random walker nationallicence periodic Markov chain nationallicence 05.40 nationallicence Revathi S. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut Balakrishnan V. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut Valsakumar M. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut Pramana Springer India 38/5(1992-05-01), 491-503 0304-4289 38:5<491 1992 38 12043 https://doi.org/10.1007/BF02847489 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02847489 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Revathi S. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut NATIONALLICENCE 700 1- Balakrishnan V. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut NATIONALLICENCE 700 1- Valsakumar M. Department of Physics, Indian Institute of Technology, 600 036, Madras, India aut NATIONALLICENCE 773 0- Pramana Springer India 38/5(1992-05-01), 491-503 0304-4289 38:5<491 1992 38 12043 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer