Newtonian diffusions and planets, with a remark on non-standard Dirichlet forms and polymers

  • S. Albeverio
  • Ph. Blanchard
  • R. Høegh-Krohn
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1095)


We discuss diffusion processes on Riemannian manifolds, for which a Newton law holds (in the stochastic sense). We emphasize the existence of a general mechanism for the formation of impenetrable barriers for these processes, corresponding to the nodes of the density of their distribution. We discuss some applications to natural phenomena like the formation of planetary systems, the morphology of galaxies, the formation of zones of winds in the atmosphere and the formation of spokes in the rings of Saturn. We also relate the recent hyperfinite theory of Dirichlet forms with the theory of local times of Brownian motion, polymer measures and the (ϕ 1 2 ϕ 2 2 )4-model of quantum field theory.


Brownian Motion Markov Process Stochastic Differential Equation Radon Measure Dirichlet Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • S. Albeverio
    • 1
  • Ph. Blanchard
    • 2
  • R. Høegh-Krohn
    • 3
    • 4
  1. 1.Mathematisches InstitutRuhr-UniversitätBochum
  2. 2.Theoretische PhysikUniversität bielefeldBielefeld
  3. 3.Centre de Physique Théorique, CNRSUniversité de ProvenceMarseille
  4. 4.Matematisk InstituttUniversitetet i OsloBlindern, Oslo

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