منابع مشابه
Critical Behaviour of Self-avoiding Walk in Five or More Dimensions
We use the lace expansion to prove that in five or more dimensions the standard self-avoiding walk on the hypercubic (integer) lattice behaves in many respects like the simple random walk. In particular, it is shown that the leading asymptotic behaviour of the number of «-step self-avoiding walks is purely exponential, that the mean square displacement is asymptotically linear in the number of ...
متن کاملThe Self-Avoiding-Walk and Percolation Critical Points in High Dimensions
We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients of the expansion are computed through order d 6 , with a rigorous error bound of order d 7 . Our method for computing terms in the expansion also applies ...
متن کاملPeculiar scaling of self-avoiding walk contacts.
The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N-->infinity they are strictly finite in number but their radius of gyration R(c) is power law distributed proportional to R(-tau)(c), where tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging length scales is ass...
متن کاملGreen’s Function for a Hierarchical Self-Avoiding Walk in Four Dimensions
This is the second of two papers on the end-to-end distance of a weakly selfrepelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times √ T log 1 8 T (
متن کاملBond - True Self - Avoiding Walk on Z
Thètrue' self-avoiding walk with bond repulsion is a nearest neighbour random walk on Z, for which the probability of jumping along a bond of the lattice is proportional to exp(?g number of previous jumps along that bond). First we prove a limit theorem for the distribution of the local time process of this walk. Using this result, later we prove a local limit theorem, as A ! 1, for the distrib...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1985
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf01206182