### Abstract

We consider a particle moving through a medium under a constant external field. The medium consists of immobile spherical obstacles of equal radii randomly distributed in ℝ^{3}. When the particle collides with an obstacle, it reflects inelastically, with restitution coefficient α , (0, 1). We study the asymptotics of X(t), the position of the particle at time t, as t → ∞. The main result is a functional limit theorem for X(t). Its proof is based on the functional CLT for Markov chains. Bibliography: 10 titles.

Original language | English (US) |
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Pages (from-to) | 6520-6534 |

Number of pages | 15 |

Journal | Journal of Mathematical Sciences |

Volume | 139 |

Issue number | 3 |

DOIs | |

State | Published - Dec 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Mathematical Sciences*,

*139*(3), 6520-6534. https://doi.org/10.1007/s10958-006-0369-2

**A functional limit theorem for the position of a particle in the Lorentz model.** / Vysotsky, V. V.

Research output: Contribution to journal › Article

*Journal of Mathematical Sciences*, vol. 139, no. 3, pp. 6520-6534. https://doi.org/10.1007/s10958-006-0369-2

}

TY - JOUR

T1 - A functional limit theorem for the position of a particle in the Lorentz model

AU - Vysotsky, V. V.

PY - 2006/12

Y1 - 2006/12

N2 - We consider a particle moving through a medium under a constant external field. The medium consists of immobile spherical obstacles of equal radii randomly distributed in ℝ3. When the particle collides with an obstacle, it reflects inelastically, with restitution coefficient α , (0, 1). We study the asymptotics of X(t), the position of the particle at time t, as t → ∞. The main result is a functional limit theorem for X(t). Its proof is based on the functional CLT for Markov chains. Bibliography: 10 titles.

AB - We consider a particle moving through a medium under a constant external field. The medium consists of immobile spherical obstacles of equal radii randomly distributed in ℝ3. When the particle collides with an obstacle, it reflects inelastically, with restitution coefficient α , (0, 1). We study the asymptotics of X(t), the position of the particle at time t, as t → ∞. The main result is a functional limit theorem for X(t). Its proof is based on the functional CLT for Markov chains. Bibliography: 10 titles.

UR - http://www.scopus.com/inward/record.url?scp=33750515660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750515660&partnerID=8YFLogxK

U2 - 10.1007/s10958-006-0369-2

DO - 10.1007/s10958-006-0369-2

M3 - Article

AN - SCOPUS:33750515660

VL - 139

SP - 6520

EP - 6534

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -