This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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 $\dot{P} + y \cdot \nabla_x P-\nabla_y \cdot E(P)- c \Delta P=0$.

Copyright 1997 American Mathematical Society

TeX source (18K)
DVI (19K)
PostScript (93K)

Article Info

• ERA Amer. Math. Soc. 03 (1997), pp. 110-113
• Publisher Identifier: S 1079-6762(97)00033-4
• 1991 Mathematics Subject Classification. Primary 58F05, 82C22, 60G55; Secondary 70H05, 60K35, 60J60
• Key words and phrases. Hamiltonian dynamics, Vlasov dynamics, Poisson point process
• Received by the editors July 28, 1997
• Posted on October 28, 1997
• Communicated by Mark Freidlin
• Comments (When Available)

Oliver Knill

Department of Mathematics, University of Arizona, Tucson, AZ 85721

E-mail address: knill@math.utexas.edu