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).
@article{ACIRM_2010__2_1_39_0,
author = {T\'oth, B\'alint and Valk\'o, Benedek},
title = {Superdiffusive bounds on self-repellent precesses in $d=2$ {\textemdash} extended abstract},
journal = {Actes des rencontres du CIRM},
pages = {39--41},
publisher = {CIRM},
volume = {2},
number = {1},
year = {2010},
doi = {10.5802/acirm.23},
zbl = {06938571},
language = {en},
url = {http://www.numdam.org/articles/10.5802/acirm.23/}
}
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 PY - 2010 SP - 39 EP - 41 VL - 2 IS - 1 PB - CIRM UR - http://www.numdam.org/articles/10.5802/acirm.23/ DO - 10.5802/acirm.23 LA - en ID - ACIRM_2010__2_1_39_0 ER -
%0 Journal Article %A Tóth, Bálint %A Valkó, Benedek %T Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract %J Actes des rencontres du CIRM %D 2010 %P 39-41 %V 2 %N 1 %I CIRM %U http://www.numdam.org/articles/10.5802/acirm.23/ %R 10.5802/acirm.23 %G en %F ACIRM_2010__2_1_39_0
Tóth, Bálint; Valkó, Benedek. Superdiffusive bounds on self-repellent precesses in $d=2$ — extended abstract. Actes des rencontres du CIRM, Tome 2 (2010) no. 1, pp. 39-41. doi : 10.5802/acirm.23. http://www.numdam.org/articles/10.5802/acirm.23/
[1] D. Amit, G. Parisi, L. Peliti: Asymptotic behavior of the ‘true’ self-avoiding walk. Physical Reviews B 27: 1635–1645 (1983) | DOI | MR
[2] R.T. Durrett, L.C.G.Rogers: Asymptotic behavior of Brownian polymers. Probability Theory and Related Fields 92: 337–349 (1992) | DOI | MR | Zbl
[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) | DOI | MR
[4] C. Landim, A. Ramirez, H-T. Yau: Superdiffusivity of two dimensional lattice gas models. Journal of Statistical Physics 119: 963–995 (2005) | DOI | MR | Zbl
[5] C. Landim, J. Quastel, M. Salmhofer, H-T. Yau: Superdiffusivity of one and two dimentsional asymmetric simple exclusion processes. Communicarions in Mathematical Physics 244: 455–481 (2004) | DOI | MR | Zbl
[6] T. S. Mountford, P. Tarrès: An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré – Probab. Stat. 44: 29–46 (2008) | DOI | Numdam | MR | Zbl
[7] J. Quastel, B. Valkó: in preparation (2010) | DOI
[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 | DOI | MR | Zbl
[9] B. Tóth: ‘True’ self-avoiding walk with bond repulsion on : limit theorems. Ann. Probab., 23: 1523-1556 (1995) | DOI | MR | Zbl
[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. | DOI | Zbl
[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 . (2010, in preparation) | DOI | MR
[12] B. Tóth, B. Vető: Continuous time ‘true’ self-avoiding random walk on . 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) | DOI | MR | Zbl
[14] H-T. Yau: law of the two dimensional asymmetric simple exclusion process. Annals of Mathematics 159: 377–105 (2004) | DOI
Cité par Sources :
