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 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.
| Original language | English (US) |
|---|---|
| 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 |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
Cite this
A functional limit theorem for the position of a particle in the Lorentz model. / Vysotsky, V. V.
In: Journal of Mathematical Sciences, Vol. 139, No. 3, 12.2006, p. 6520-6534.Research output: Contribution to journal › Article
}
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 -