Physics – Mathematical Physics
Scientific paper
2002-05-20
Communications in Mathematical Physics 239, 523-547 (2003)
Physics
Mathematical Physics
29 pages, v2: references
Scientific paper
10.1007/s00220-003-0885-6
In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that at the critical killing rate (mass-squared) \beta^c, the Green's function behaves like the free one. - Now we analyze the end-to-end distance of the model and show that its expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log log T)/log T)), which is the same law as has been conjectured for self-avoiding walks on the simple cubic lattice Z^4. The proof uses inverse Laplace transforms to obtain the end-to-end distance from the Green's function, and requires detailed properties of the Green's function throughout a sector of the complex \beta plane. These estimates are derived in a companion paper [math-ph/0205028].
Brydges David C.
Imbrie John Z.
No associations
LandOfFree
End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions 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 End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-242567