Journal of Mathematical Physics
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
Restricted partition functions of the two-dimensional Ising model on a half-infinite cylinder
We study the Ising model on a half-infinite cylinder at the critical temperature. On the boundary circle, we fix four intervals of constant signs. Let 1, 2, 3, and 4 be the positions where the flips o...
Next Article
Fine structure of the asymptotic expansion of cyclic integrals
The asymptotic expansion of n-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explic...

Total current fluctuations in the asymmetric simple exclusion process

J. Math. Phys. 50, 095204 (2009); doi:10.1063/1.3136630

Published 8 June 2009

You are logged in to this journal.

Craig A. Tracy1 and Harold Widom2
1Department of Mathematics, University of California, Davis, California 95616, USA
2Department of Mathematics, University of California, Santa Cruz, California 95064, USA
A limit theorem for the total current in the asymmetric simple exclusion process (ASEP) with step initial condition is proven. This extends the result of Johansson on TASEP to ASEP. ©2009 American Institute of Physics
History: Received 4 February 2009; accepted 17 March 2009; published 8 June 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/095204/1
FULL TEXT OPTIONS   (FREE)
Download PDF (68 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 05.40.-a
    Fluctuation phenomena, random processes, noise, and Brownian motion
  • 02.50.Ga
    Markov processes
  • 02.50.Cw
    Probability theory
  • YEAR: 2009

RELATED DATABASES

Web of Science

View this record in Web of Science

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (15)
View in Separate Window/Tab
  1. Balázs, M., Komjáthy, J., and Seppäläinen, T., “Microscopic concavity and fluctuation bounds in a class of deposition processes,” e-print arXiv:0808.1177.
  2. Balázs, M. and Seppäläinen, T., “Order of current variance and diffusivity in the asymmetric simple exclusion process,” Ann. Math. (to be published).
  3. Balázs, M. and Seppäläinen, T., “Fluctuation bounds for the asymmetric simple exclusion process,” ALEA Lat. Am. J. Probab. Math. Stat. 6, 1 (2009).
  4. Golinelli, O. and Mallick, K., “The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics,” J. Phys. A 39, 12679 (2006).
  5. Johansson, K., “Shape fluctuations and random matrices,” Commun. Math. Phys. 209, 437 (2000).
  6. Kardar, M., Parisi, G., and Zhang, Y. -C., “Dynamic scaling of growing interfaces,” Phys. Rev. Lett. 56, 889 (1986). [MEDLINE]
  7. Liggett, T. M., Interacting Particle Systems (Springer, Berlin, 2005) (reprint of the 1985 original).
  8. Liggett, T. M., Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Springer, Berlin, 1999).
  9. Quastel, J. and Valkó, B., “Superdiffusivity of finite-range asymmetric exclusion processes on t1/3 [openface Z],” Commun. Math. Phys. 273, 379 (2007).
  10. Seppäläinen, T., “Directed random growth models on the plane,” e-print arXiv:0708.2721.
  11. Soshnikov, A., “Determinantal random fields,” Russ. Math. Surveys 55, 923 (2000). [ISI]
  12. Spitzer, F., “Interaction of Markov processes,” Adv. Math. 5, 246 (1970).
  13. Spohn, H., “Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals,” Physica A 369, 71 (2006).
  14. Tracy, C. A. and Widom, H., “Level-spacing distributions and the Airy kernel,” Commun. Math. Phys. 159, 151 (1994). [ISI]
  15. Tracy, C. A. and Widom, H., “Asymptotics in ASEP with step initial condition,” e-print arXiv:0807.1713.

Copyright © American Institute of Physics