Mathematics – Probability
Scientific paper
2010-12-28
Mathematics
Probability
21 pages
Scientific paper
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient of its own occupation time measure (local time). The second example is a diffusion in a fixed random environment given by the curl of massless Gaussian free field. In both cases we show that the process is superdiffusive: the variance grows faster than linearly with time. We give lower and upper bounds of the order of t log log t, respectively, t log t. We also present computations for an anisotropic version of the self-repelling Brownian polymer where we give lower and upper bounds of t (log t)^{1/2}, respectively, t log t. The bounds are given in the sense of Laplace transforms, the proofs rely on the resolvent method. The true order of the variance for these processes is expected to be t (log t)^{1/2} for the isotropic and t (log t)^{2/3} for the non-isotropic case. In the appendix we present a non-rigorous derivation of these scaling exponents.
Toth Balint
Valkó Benedek
No associations
LandOfFree
Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-427707