# 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

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topTóth, 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

top- D. Amit, G. Parisi, L. Peliti: Asymptotic behavior of the ‘true’ self-avoiding walk. Physical Reviews B27: 1635–1645 (1983) MR690540
- R.T. Durrett, L.C.G.Rogers: Asymptotic behavior of Brownian polymers. Probability Theory and Related Fields92: 337–349 (1992) Zbl0767.60080MR1165516
- 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)
- C. Landim, A. Ramirez, H-T. Yau: Superdiffusivity of two dimensional lattice gas models. Journal of Statistical Physics119: 963–995 (2005) Zbl1088.82016MR2157854
- 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
- T. S. Mountford, P. Tarrès: An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré – Probab. Stat.44: 29–46 (2008) Zbl1175.60084MR2451570
- J. Quastel, B. Valkó: in preparation (2010)
- 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
- B. Tóth: ‘True’ self-avoiding walk with bond repulsion on $\mathbb{Z}$: limit theorems. Ann. Probab., 23: 1523-1556 (1995) Zbl0852.60083MR1379158
- 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
- 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
- B. Tóth, B. Vető: Continuous time ‘true’ self-avoiding random walk on $\mathbb{Z}$. ALEA – Latin Amrican Journal of Probability (2010, to appear) http://arxiv.org/abs/0909.3863
- B. Tóth, W. Werner: The true self-repelling motion. Probab. Theory Rel. Fields, 111: 375-452 (1998) Zbl0912.60056MR1640799
- H-T. Yau: ${(logt)}^{2/3}$ law of the two dimensional asymmetric simple exclusion process. Annals of Mathematics159: 377–105 (2004) Zbl1060.60099MR2052358

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