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

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Stochastic Analysis and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1095))

Abstract

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 21 ϕ 22 )4-model of quantum field theory.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Ruhr-Universität, D-4630, Bochum

    S. Albeverio

  2. Theoretische Physik, Universität bielefeld, D-4800, Bielefeld

    Ph. Blanchard

  3. Centre de Physique Théorique, CNRS, Université de Provence, F-13288, Marseille

    R. Høegh-Krohn

  4. Matematisk Institutt, Universitetet i Oslo, Blindern, Oslo

    R. Høegh-Krohn

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  1. S. Albeverio
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  2. Ph. Blanchard
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  3. R. Høegh-Krohn
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Aubrey Truman David Williams

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Albeverio, S., Blanchard, P., Høegh-Krohn, R. (1984). Newtonian diffusions and planets, with a remark on non-standard Dirichlet forms and polymers. In: Truman, A., Williams, D. (eds) Stochastic Analysis and Applications. Lecture Notes in Mathematics, vol 1095. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099118

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  • DOI: https://doi.org/10.1007/BFb0099118

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