منابع مشابه
Bond - 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...
متن کاملOn the scaling limit of planar self - avoiding walk
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no self-intersection. In this paper we present conjectures for the scaling limit of the uniform measures on these objects. The conjectures are based on recent results on the stochastic Loewner evolution and nondisconnecting...
متن کاملNew Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice Zd. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high d, and in fact agree with the rst four terms of the 1=d expansion for the connective constant. The bounds are the best t...
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 کاملA Self-avoiding Walk with Attractive Interactions
A powerful tool for the study of self-avoiding walks is the lace expansion of Brydges and Spencer [BS]. It is applicable above four dimensions and shows the mean-field behavior of self-avoiding walks, that is, critical exponents are those of the simple random walk. An extensive survey of random walks can be found in [MS]. The lace expansion was originally introduced for weakly self-avoiding wal...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2020
ISSN: 0025-5645
DOI: 10.2969/jmsj/82588258