Skip to main content
SpringerLink
Log in

Hydrodynamic Limit for a Zero-Range Process in the Sierpinski Gasket

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider a system of random walks on graph approximations of the Sierpinski gasket, coupled with a zero-range interaction. We prove that the hydrodynamic limit of this system is given by a nonlinear heat equation on the Sierpinski gasket.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barlow M.T., Perkins E.A.: Brownian motion on the Sierpiński gasket. Probab. Theory Related Fields 79(4), 543–623 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chang C.C., Yau H.-T.: Fluctuations of one-dimensional Ginzburg-Landau models in nonequilibrium. Commun. Math. Phys. 145(2), 209–234 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Gravner J., Quastel J.: Internal DLA and the Stefan problem. Ann. Probab. 28(4), 1528–1562 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Guo M.Z., Papanicolaou G.C., Varadhan S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys. 118(1), 31–59 (1988)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Jara, M.D., Landim, C., Sethuraman, S.: Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes. Probab. Theory Relat. Fields, to appear, doi:10.1007/s00440-008-0178-2, 2008

  6. Kigami J.: Analysis on fractals, Volume 143 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  7. Kigami J.: Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate. Math. Ann. 340(4), 781–804 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kigami J., Sheldon D.R., Strichartz R.S.: Green’s functions on fractals. Fractals 8(4), 385–402 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kipnis, C., Landim, C.: Scaling limits of interacting particle systems, Volume 320 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 1999

  10. Kusuoka S.: Dirichlet forms on fractals and products of random matrices. Publ. Res. Inst. Math. Sci. 25(4), 659–680 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  11. Yau H.-T.: Relative entropy and hydrodynamics of Ginzburg-Landau models. Lett. Math. Phys. 22(1), 63–80 (1991)

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FYMA, Université Catholique de Louvain, chemin du Cyclotron 2, B-1348, Louvain-la-Neuve, Belgium

    Milton Jara

Authors
  1. Milton Jara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Milton Jara.

Additional information

Communicated by H. Spohn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jara, M. Hydrodynamic Limit for a Zero-Range Process in the Sierpinski Gasket. Commun. Math. Phys. 288, 773–797 (2009). https://doi.org/10.1007/s00220-009-0746-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-009-0746-z

Keywords

Search

Navigation