Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
The Initial Drift of a 2D Droplet at Zero Temperature
Download PDF
Download PDF
  • Published: 21 June 2006

The Initial Drift of a 2D Droplet at Zero Temperature

  • Raphaël Cerf1 &
  • Sana Louhichi1 

Probability Theory and Related Fields volume 137, pages 379–428 (2007)Cite this article

  • 72 Accesses

  • 4 Citations

  • Metrics details

Abstract

We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. We compute the explicit value of this coefficient.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Andjel E.D. (1982). Invariant measures for the zero range process. Ann. Probab. 10(3): 525–547

    MathSciNet  Google Scholar 

  2. Chayes L., Swindle G. (1996). Hydrodynamic limits for one-dimensional particle systems with moving boundaries. Ann. Probab. 24(2): 559–598

    Article  MathSciNet  Google Scholar 

  3. Chayes L., Schonmann R.H., Swindle G. (1995). Lifshitz’ law for the volume of a two-dimensional droplet at zero temperature. J. Stat. Phys. 79(5–6): 821–831

    Article  MathSciNet  Google Scholar 

  4. De Masi A., Orlandi E., Presutti E., Triolo L. (1993). Motion by curvature by scaling nonlocal evolution equations. J. Stat. Phys. 73(3–4): 543–570

    Article  Google Scholar 

  5. De Masi A., Orlandi E., Presutti E., Triolo L. (1994). Glauber evolution with the Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics. Nonlinearity 7(3): 633–696

    Article  MathSciNet  Google Scholar 

  6. Katsoulakis M.A., Souganidis P.E. (1995). Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interactions and Glauber dynamics. Commun. Math. Phys. 169(1): 61–97

    Article  MathSciNet  Google Scholar 

  7. Katsoulakis M.A., Souganidis P.E. (1997). Stochastic Ising models and anisotropic front propagation. J. Stat. Phys. 87(1–2): 63–89

    Article  MathSciNet  Google Scholar 

  8. Petrov V.V. (1995). Limit theorems of probability theory: sequences of independent random variables. Clarendon Press, Oxford

    MATH  Google Scholar 

  9. Sowers R.B. (1999). Hydrodynamical limits and geometric measure theory: mean curvature limits from a threshold voter model. J. Funct. Anal. 169(2): 421–455

    Article  MathSciNet  Google Scholar 

  10. Spohn H. (1993). Interface motion in models with stochastic dynamics. J. Stat. Phys. 71(5–6): 1081–1132

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Paris-Sud, Probabilités, statistique et modélisation, Bât. 425, 91405, Orsay Cedex, France

    Raphaël Cerf & Sana Louhichi

Authors
  1. Raphaël Cerf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sana Louhichi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sana Louhichi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cerf, R., Louhichi, S. The Initial Drift of a 2D Droplet at Zero Temperature. Probab. Theory Relat. Fields 137, 379–428 (2007). https://doi.org/10.1007/s00440-006-0007-4

Download citation

  • Received: 24 November 2004

  • Revised: 16 March 2006

  • Published: 21 June 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0007-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • 2D Ising model
  • Glauber dynamics
  • Zero temperature
  • Markov process
  • Mean curvature
  • Velocity

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature