• First passage time distributions for finite one-dimensional random walks

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      https://www.ias.ac.in/article/fulltext/pram/021/02/0111-0122

    • Keywords

       

      Biased random walks; Markov processes; first passage time; finite chains

    • Abstract

       

      We present closed expressions for the characteristic function of the first passage time distribution for biased and unbiased random walks on finite chains and continuous segments with reflecting boundary conditions. Earlier results on mean first passage times for one-dimensional random walks emerge as special cases. The divergences that result as the boundary is moved out to infinity are exhibited explicitly. For a symmetric random walk on a line, the distribution is an elliptic theta function that goes over into the known Lévy distribution with exponent 1/2 as the boundary tends to ∞.

    • Author Affiliations

       

      M Khantha1 V Balakrishnan1

      1. Department of Physics, Indian Institute of Technology, Madras - 600 036, India
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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