Geodesic
A deterministic displacement theorem for Poisson processes
Knill, Oliver1, 2
1 Department of Mathematics, University of Arizona, Tucson, AZ 85721
2 Department of Mathematics, University of Texas, Austin, TX 78712
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 110-113 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

We announce a deterministic analog of Bartlett’s displacement theorem. The result is that a Poisson property is stable with respect to deterministic Hamiltonian displacements. While the random point configurations move according to an $n$-body evolution, the mean measure $P$ satisfies a nonlinear Vlasov type equation $\dot {P} + y \cdot \nabla _x P - \nabla _y \cdot E(P) = 0$. Combined with Bartlett’s theorem, the result generalizes to interacting Brownian particles, where the mean measure satisfies a McKean-Vlasov type diffusion equation $\dot {P} + y \cdot \nabla _x P-\nabla _y \cdot E(P)- c \Delta P=0$.
DOI : 10.1090/S1079-6762-97-00033-4

Knill, Oliver 1, 2

1 Department of Mathematics, University of Arizona, Tucson, AZ 85721
2 Department of Mathematics, University of Texas, Austin, TX 78712 
@article{10_1090_S1079_6762_97_00033_4,
     author = {Knill, Oliver},
     title = {A deterministic displacement theorem for {Poisson} processes},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {110--113},
     year = {1997},
     volume = {03},
     doi = {10.1090/S1079-6762-97-00033-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00033-4/}
}
TY  - JOUR
AU  - Knill, Oliver
TI  - A deterministic displacement theorem for Poisson processes
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1997
SP  - 110
EP  - 113
VL  - 03
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00033-4/
DO  - 10.1090/S1079-6762-97-00033-4
ID  - 10_1090_S1079_6762_97_00033_4
ER  - 
%0 Journal Article
%A Knill, Oliver
%T A deterministic displacement theorem for Poisson processes
%J Electronic research announcements of the American Mathematical Society
%D 1997
%P 110-113
%V 03
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00033-4/
%R 10.1090/S1079-6762-97-00033-4
%F 10_1090_S1079_6762_97_00033_4
Knill, Oliver. A deterministic displacement theorem for Poisson processes. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 110-113. doi: 10.1090/S1079-6762-97-00033-4

[1] Bunimovich, L. A., Cornfeld, I. P., Dobrushin, R. L., Jakobson, M. V., Maslova, N. B., Pesin, Ya. B., Sinaĭ, Ya. G., Sukhov, Yu. M., Vershik, A. M. Dynamical systems. II 1989

[2] Kingman, J. F. C. Poisson processes 1993

Cité par Sources :