Superdiffusive bounds on self-repellent precesses in d = 2 — extended abstract

Bálint Tóth[1]; Benedek Valkó[2]

  • [1] Institute of Mathematics, Budapest University of Technology, Egry József u. 1, Budapest 1111, Hungary
  • [2] Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Drive, Madison WI 53706

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 1, page 39-41
  • ISSN: 2105-0597

Abstract

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We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).

How to cite

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Tóth, Bálint, and Valkó, Benedek. "Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract." Actes des rencontres du CIRM 2.1 (2010): 39-41. <http://eudml.org/doc/115849>.

@article{Tóth2010,
abstract = {We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).},
affiliation = {Institute of Mathematics, Budapest University of Technology, Egry József u. 1, Budapest 1111, Hungary; Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Drive, Madison WI 53706},
author = {Tóth, Bálint, Valkó, Benedek},
journal = {Actes des rencontres du CIRM},
keywords = {self-repelling random motion; diffusion in random environment; super-diffusivity; Gaussian free field},
language = {eng},
month = {12},
number = {1},
pages = {39-41},
publisher = {CIRM},
title = {Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract},
url = {http://eudml.org/doc/115849},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Tóth, Bálint
AU - Valkó, Benedek
TI - Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract
JO - Actes des rencontres du CIRM
DA - 2010/12//
PB - CIRM
VL - 2
IS - 1
SP - 39
EP - 41
AB - We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).
LA - eng
KW - self-repelling random motion; diffusion in random environment; super-diffusivity; Gaussian free field
UR - http://eudml.org/doc/115849
ER -

References

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  1. D. Amit, G. Parisi, L. Peliti: Asymptotic behavior of the ‘true’ self-avoiding walk. Physical Reviews B27: 1635–1645 (1983) MR690540
  2. R.T. Durrett, L.C.G.Rogers: Asymptotic behavior of Brownian polymers. Probability Theory and Related Fields92: 337–349 (1992) Zbl0767.60080MR1165516
  3. I. Horváth, B. Tóth, B. Vető: Diffusive limits for “true” (or myopic) self-avoiding random walks and self-repellent Brownian polymers in three and more dimensions. http://arxiv.org/abs/1009.0401 (submitted, 2010) 
  4. C. Landim, A. Ramirez, H-T. Yau: Superdiffusivity of two dimensional lattice gas models. Journal of Statistical Physics119: 963–995 (2005) Zbl1088.82016MR2157854
  5. C. Landim, J. Quastel, M. Salmhofer, H-T. Yau: Superdiffusivity of one and two dimentsional asymmetric simple exclusion processes. Communicarions in Mathematical Physics244: 455–481 (2004) Zbl1064.60164MR2034485
  6. T. S. Mountford, P. Tarrès: An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré – Probab. Stat.44: 29–46 (2008) Zbl1175.60084MR2451570
  7. J. Quastel, B. Valkó: in preparation (2010) 
  8. P. Tarrès, B. Tóth, B. Valkó: Diffusivity bounds for 1d Brownian polymers. Annals of Probability (to appear 2010+) http://arxiv.org/abs/0911.2356 Zbl1242.60105
  9. B. Tóth: ‘True’ self-avoiding walk with bond repulsion on ℤ : limit theorems. Ann. Probab., 23: 1523-1556 (1995) Zbl0852.60083MR1379158
  10. B. Tóth: Self-interacting random motions. In: Proceedings of the 3rd European Congress of Mathematics, Barcelona 2000, vol. 1, pp. 555-565, Birkhauser, 2001. Zbl1101.82011MR1905343
  11. P. Tarrès, B. Tóth, B. Valkó: Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the free Gaussian field in d = 2 . (2010, in preparation) Zbl1245.82092
  12. B. Tóth, B. Vető: Continuous time ‘true’ self-avoiding random walk on ℤ . ALEA – Latin Amrican Journal of Probability (2010, to appear) http://arxiv.org/abs/0909.3863 
  13. B. Tóth, W. Werner: The true self-repelling motion. Probab. Theory Rel. Fields, 111: 375-452 (1998) Zbl0912.60056MR1640799
  14. H-T. Yau: ( log t ) 2 / 3 law of the two dimensional asymmetric simple exclusion process. Annals of Mathematics159: 377–105 (2004) Zbl1060.60099MR2052358

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