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.

Voir la notice de l'article provenant de la source American Mathematical Society

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 
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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. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00033-4/

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

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