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From Non-symmetric Particle Systems to Non-linear PDEs on Fractals

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Stochastic Partial Differential Equations and Related Fields (SPDERF 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 229))

Abstract

We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear heat equation. We discuss a joint density-current law of large numbers and a corresponding large deviation principle.

Research supported in part by NSF grants 1262929, 1613025.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Colgate University, Hamilton, NY, 13346, USA

    Joe P. Chen

  2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Michael Hinz

  3. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA

    Alexander Teplyaev

Authors
  1. Joe P. Chen
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  2. Michael Hinz
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  3. Alexander Teplyaev
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Corresponding author

Correspondence to Alexander Teplyaev .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Andreas Eberle

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  3. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Walter Hoh

  4. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Moritz Kassmann

  5. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Wilhelm Stannat

  6. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

    Gerald Trutnau

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Chen, J.P., Hinz, M., Teplyaev, A. (2018). From Non-symmetric Particle Systems to Non-linear PDEs on Fractals. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_34

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