End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions

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dc.creatorBrydges, David C.
dc.creatorImbrie, John Z.
dc.date2002-05-20
dc.date2002-06-06
dc.date.accessioned2026-07-07T04:29:12Z
dc.date.available2026-07-07T04:29:12Z
dc.descriptionIn [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) β^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 βplane. These estimates are derived in a companion paper [math-ph/0205028].
dc.description29 pages, v2: references
dc.identifierhttps://arxiv.org/abs/math-ph/0205027
dc.identifierhttp://arxiv.org/abs/math-ph/0205027
dc.identifierCommunications in Mathematical Physics 239, 523-547 (2003)
dc.identifierdoi:10.1007/s00220-003-0885-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57068
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subject82B41, 82B28, 82B27, 81T60, 81T17, 60K35, 60G18
dc.titleEnd-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions
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