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
Brownian confinement and pinning in a Poissonian potential. II
Download PDF
Download PDF
  • Published: March 1996

Brownian confinement and pinning in a Poissonian potential. II

  • Alain-Sol Sznitman1 

Probability Theory and Related Fields volume 105, pages 31–56 (1996)Cite this article

  • 61 Accesses

  • 3 Citations

  • Metrics details

Summary

We continue our study ofd-dimensional Brownian motion in a soft repulsive Poissonian potential over a long time interval [0,t]. We prove here a pinning effect: for typical configuratons, with probability tending to 1 ast tends to ∞, the particle gets trapped close to locations of near minima of certain variational problems. These locations lie at distances growing almost linearly witht from the origin, and the particle gets pinned within distance smaller than any positive power oft of one such location. In dimension 1, we can push further our estimates and show that in a suitable sense, the particle gets trapped with high probability, within time ∈t and within distance (logt)2+∈ from a suitable location at distance of ordert/(logt)3 from the origin.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Krug, J., Halpin Healy, T.: Directed polymer in the presence of columnar disorder. J. Phys. I, France3, 2179–2198 (1993)

    Google Scholar 

  2. Sznitman, A.S.: Brownian motion in a Poissonian potential. Probab. Theory Relat. Fields97, 447–477 (1993)

    Google Scholar 

  3. Sznitman, A.S.: Quenched critical large deviations for Brownian motion in a Poissonian potential. J. Funct. Anal.131(1), 54–77 (1995)

    Google Scholar 

  4. Sznitman, A.S.: Brownian confinement and pinning in a Poissonian potential. I. Probab. Theory Relat. Fields105, 1–29 (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Alain-Sol Sznitman

Authors
  1. Alain-Sol Sznitman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article was processed by the author using the LATEX style filepljour1m from Springer-Verlag

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sznitman, AS. Brownian confinement and pinning in a Poissonian potential. II. Probab. Th. Rel. Fields 105, 31–56 (1996). https://doi.org/10.1007/BF01192070

Download citation

  • Received: 24 October 1994

  • Revised: 05 December 1995

  • Issue Date: March 1996

  • DOI: https://doi.org/10.1007/BF01192070

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

Mathematics Subject Classification (1991)

  • 60K40
  • 82D30
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