منابع مشابه
Peculiar 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...
متن کاملEfficient modularity optimization by self-avoiding walk
Different kinds of random walks have showed to be useful in the study of the structural properties of complex networks. Among them, the restricted dynamics of the self-avoiding random walk (SAW), which reaches only unvisited vertices in the same walk, has been succesfully used in network exploration. SAWs are therefore a promising tool to investigate community structures in networks. Despite it...
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...
متن کاملFunctional integral representations for self-avoiding walk
Abstract: We give a survey and unified treatment of functional integral representations for both simple random walk and some self-avoiding walk models, including models with strict self-avoidance, with weak selfavoidance, and a model of walks and loops. Our representation for the strictly self-avoiding walk is new. The representations have recently been used as the point of departure for rigoro...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2019
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-018-00898-7