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
Large deviations for a reaction diffusion model
Download PDF
Download PDF
  • Published: September 1993

Large deviations for a reaction diffusion model

  • G. Jona-Lasinio1,
  • C. Landim2 &
  • M. E. Vares3 

Probability Theory and Related Fields volume 97, pages 339–361 (1993)Cite this article

  • 351 Accesses

  • Metrics details

Summary

We obtain large deviation estimates for the empirical measure of a class of interacting particle systems. These consist of a superposition of Glauber and Kawasaki dynamics and are described, in the hydrodynamic limit, by a reaction diffusion equation. We extend results of Kipnis, Olla and Varadhan for the symmetric exclusion process, and provide an approximation scheme for the rate functional. Some physical implications of our results are briefly indicated.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • [DFL] De, Masi A., Ferrari, P., Lebowitz, J.: Reaction diffusion equations for interacting particle systems. J. Stat. Phys.55, 523–578 (1986)

    Google Scholar 

  • [DPS] De, Masi A., Presutti, E., Scacciatelli, E.: The weakly asymmetric simple exclusion process. Ann. Inst. H. Poincaré25, 1–38 (1989)

    Google Scholar 

  • [DS] Deuschel, J.D., Stroock, D.W.: Large deviations. New York: Academic Press 1989

    Google Scholar 

  • [DV1] Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time I. Commun. Pure Appl. Math.28, 1–49 (1975)

    Google Scholar 

  • [DV2] Donsker, M.D., Varadhan S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time II. Commun. Pure Appl. Math.28, 279–303 (1975)

    Google Scholar 

  • [DV3] Donsker, M.D., Varadhan S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time III. Commun. Pure Appl. Math.29, 389–463 (1976)

    Google Scholar 

  • [GPV] Guo, M.Z., Papanicolau, G.C., Varadhan, S.R.S.: Non linear diffusion limit for a system with nearest neighbour interactions. Commun. Math. Phys.118, 31–59 (1988)

    Google Scholar 

  • [J] Jona-Lasinio G.: Stochastic reaction diffusion equations and interacting particle systems. Ann. Inst. H. Poincaré, Phys. Théorique55, 751–758 (1991)

    Google Scholar 

  • [KOV] Kipnis, C., Olla, S., Varadhan, S.R.S.: Hydrodynamics and large deviations for simple exclusion processes. Commun. Pure Appl. Math.42, 115–137 (1989)

    Google Scholar 

  • [L1] Landim, C.: Occupation time large deviations of the symmetric simple exclusion process. Ann. Probab.20, 206–231 (1992)

    Google Scholar 

  • [L2] Landim, C.: An overview on large deviations for the empirical measure of interacting particle systems. Ann. Inst. H. Poincaré, Phys. Théorique55, 615–635 (1991)

    Google Scholar 

  • [O] Oelschläger, K.: A law of large numbers for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheor. Verw. Geb.69, 279–322 (1985)

    Google Scholar 

  • [On] Onsager, L.: Reciprocal relations in irreversible processes I and II. Phys. Rev.37, 405 (1991); Phys. Rev.38, 2265 (1991)

    Google Scholar 

  • [OM] Onsager, L., Machlup, S.: Fluctuations and irreversible processes I and II. Phys. Rev.91, 1505 (1953);91, 1512 (1953)

    Google Scholar 

  • [V] Varadhan, S.R.S.: Large Deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 46 Philadelphia: SIAM 1984

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 1-00185, Roma, Italy

    G. Jona-Lasinio

  2. Faculté de Sciences, LAMS de l'Université de Rouen, BP 118, F-76134, Mont-Saint-Aignan Cedex, France

    C. Landim

  3. IMPA, Estrada Dona Castorina 110, J. Botânico, 22460, Rio de Janeiro, RJ, Brazil

    M. E. Vares

Authors
  1. G. Jona-Lasinio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Landim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. E. Vares
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jona-Lasinio, G., Landim, C. & Vares, M.E. Large deviations for a reaction diffusion model. Probab. Th. Rel. Fields 97, 339–361 (1993). https://doi.org/10.1007/BF01195070

Download citation

  • Received: 23 July 1991

  • Revised: 04 May 1993

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01195070

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

  • 60K35
  • 82A05
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