### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 599-614 |

Number of pages | 16 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 100 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1980 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*100*(3), 599-614. https://doi.org/10.1016/0378-4371(80)90170-3

**Reactions governed by a binomial redistribution process-The ehrenfest urn problem.** / Schulten, Klaus; Schulten, Zan; Szabo, Attila.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 100, no. 3, pp. 599-614. https://doi.org/10.1016/0378-4371(80)90170-3

}

TY - JOUR

T1 - Reactions governed by a binomial redistribution process-The ehrenfest urn problem

AU - Schulten, Klaus

AU - Schulten, Zan

AU - Szabo, Attila

PY - 1980/3

Y1 - 1980/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=45949128287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45949128287&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(80)90170-3

DO - 10.1016/0378-4371(80)90170-3

M3 - Article

AN - SCOPUS:45949128287

VL - 100

SP - 599

EP - 614

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3

ER -