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Reactions governed by a binomial redistribution process—The ehrenfest urn problem

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  • Schulten, Klaus
  • Schulten, Zan
  • Szabo, Attila

Abstract

A distributive process of the binomial type in a one-dimensional discrete space with an absorbing barrier is studied. A simple expression for the particle number Σ(t) is derived. The analysis is based on recursion relationships and sum rules for the underlying eigenvectors, the Krawtchouk polynomials. The first passage time is determined, and the validity of the passage time approximation to Σ(t) tested. The continuous limit, corresponding to the diffusion and reaction of a harmonically bound particle, is briefly described.

Suggested Citation

  • Schulten, Klaus & Schulten, Zan & Szabo, Attila, 1980. "Reactions governed by a binomial redistribution process—The ehrenfest urn problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(3), pages 599-614.
    • Handle: RePEc:eee:phsmap:v:100:y:1980:i:3:p:599-614
    DOI: 10.1016/0378-4371(80)90170-3
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    Cited by:

    1. Coffey, W.T. & Crothers, D.S.F. & Waldron, J.T., 1994. "Integral representation of exact solutions for the correlation times of rotators in periodic potentials — derivation of asymptotic expansions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(3), pages 600-626.
    2. Saravanan, Rajendran & Chakraborty, Aniruddha, 2019. "Reaction–diffusion system: Fate of a Gaussian probability distribution on flat potential with a sink," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    3. Weiss, George H. & Szabo, Attila, 1983. "First passage time problems for a class of master equations with separable kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(3), pages 569-579.

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