S. Caracciolo, G. Parisi and A. Pelissetto, Random walks with short-range interaction and mean-eld behavior, J. Stat. Phys. 77: 519-543 , 1994. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
A Survey of One-Dimensional Random Polymers - van der Hofstad, König (2000) (Correct)
....: bn =2cg, and compared the probability for S to have no self intersections to the probability that S n = O(n ) This argument was strongly criticized by des Cloiseaux [Cl75] However, a more careful analysis, using a mean eld approximation, yielded the worse result (3) 2=3. See [CPP94] for an explanation of the heuristic method of des Cloiseaux. Our neglect of the short loops in the heuristics above is considered harmless since it is the suppression of long loops that dictates the scale of the polymer. Indeed, if we would only incorporate loops of length less than or equal to m ....
....expected end toend distance of the polymer, EQn jS n j, is of interest. This model contains some avor of the two dimensional polymer model since it requires some control on the structure of the set of time pairs at which self intersections occur (but not only on their number) Caracciolo et al. [CPP94] conjecture that the critical exponent (1) 1; p) in (1.21) assumes the values (1) minf2 p; 1g for p 3 2 1 2 for p 3 2 : 2.8) Hence, one expects that the polymer behaves di usively for p 3 2 (with logarithmic corrections for p = 3 2 ) and ballistically for p 1 and the ....
S. Caracciolo, G. Parisi and A. Pelissetto, Random walks with short-range interaction and mean-eld behavior, J. Stat. Phys. 77, 519-543, 1994.
The Diffusive Phase of a Model of Self-Interacting Walks - Brydges, Slade (1997) (5 citations) (Correct)
....when p = 3 2 by Theorem 1.3, and presumably for p 2 (0; 3 2 ) the behaviour of the walk interpolates between these two extremes as in (1. 21) Related issues for the model in which the energy function T Gammap J T is replaced by P 0i jT jj Gamma ij Gammap ffi (i) j) are discussed in [13, 17]. A different type of attractive walk model was studied in [35] in which the weight of a T step walk is given by exp 2 4 fi T X j=0 I[ j) i) for some i j] 3 5 : 1.22) For this model, T Gamma1=3 (T ) converges to a continuous random variable as T 1. The interaction here is ....
S. Caracciolo, G. Parisi, and A. Pelissetto. Random walks with short-range interaction and mean-field behavior. Preprint, (1994).
A New Inductive Approach to the Lace Expansion for .. - van der Hofstad.. (1997) (2 citations) (Correct)
....lower dimensions at the cost of sufficiently lowering the penalty of long loops. In addition, we prove a local central limit theorem for d 4, p 0 and for d 4, p 4 Gammad 2 . This leaves open the important case d 4, p = 0. Other aspects of the model have been studied by Caracciolo et al. [2] and Kennedy [9] Several approaches to the lace expansion for self avoiding walks have appeared previously in the literature, the principal difference between the approaches being the methods used to obtain convergence of the expansion. Brydges and Spencer [1] used induction on finite memory and ....
S. Caracciolo, G. Parisi, and A. Pelissetto. Random walks with short-range interaction and mean-field behavior. J. Stat. Phys., 77:519--543, (1994).
A Faster Implementation of the Pivot Algorithm for Self-Avoiding.. - Kennedy (2001) (Correct)
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S. Caracciolo, G. Parisi and A. Pelissetto, Random walks with short-range interaction and mean-eld behavior, J. Stat. Phys. 77: 519-543 , 1994.
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