Hara, T. (1990). Mean-field critical behaviour for correlation length for percolation in high dimensions. Probab. Theor. Relat. Fields, 86:337--385. Home/Search Document Not in Database Summary Related Articles Check |
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Mean-field Critical Behavior for Contact Processes - Sakai (2000) (Correct)
....x = x 1 ; x 2 ; Delta Delta Delta ; x d ) and I E denotes the indicator function of the condition E which takes the value 1 if the condition E is satisfied and 0 otherwise. Remark 2.1. We can consider a more general class for the spatially spread out contact process. See for the references [13], 14] and [20] From now on we use upper case letters for points in Z d Theta R. Particularly we use O to denote the space time origin. For X 2 Z d Theta R, we write oe(X) and (X) for the spatial and the temporal components of X respectively. X is said to be connected to Y (equivalently Y ....
.... to WG (X) with X 6= O are bounded by d X j=1 Z Pi d Theta Pi 1 dK ( 2 ) d 1 Phi j b D(k) Psi 2 n 1 p 2 Phi 1 Gamma b D(k) 2 3 j j Psi o 4 d X j=1 Z Pi d d d k ( 2 ) d 18 Phi j b D(k) Psi 2 Phi 1 Gamma b D(k) Psi 3 : In Appendix B of [13] and Appendix A of [19] it has been proved that the right hand side is bounded by a d independent multiple of ( d Gamma 4 ) Gamma1 for the nearest neighbor model, or by a L independent multiple of L 2 Gammad (ln L) d for the spread out model. The contribution from the second term of ....
Hara, T.: Mean-field critical behaviour for correlation length for percolation in high dimensions. Probab. Theory Rel. Fields, 86, 337--385 (1990)
The scaling limit of the incipient infinite cluster in.. - Hara, Slade (1999) (5 citations) Self-citation (Hara) (Correct)
....for the spread out model for d 6andL su#ciently large. We subsequently showed that d # 19 is large enough for the nearest neighbour model [6] Thus the above critical exponents are known to exist, and to take on the corresponding values for a tree, in these contexts. In addition, it was shown in [7] that the critical exponent # for the correlation length is equal to 1 2 , in the sense of upper and lower bounds with di#erent constants, for the nearest neighbour model in su#ciently high dimensions and for su#ciently spread out models for d 6. In this paper, we extend some of the above ....
T. Hara. Mean field critical behaviour for correlation length for percolation in high dimensions. Prob. Th. and Rel. Fields, 86:337--385, (1990).
New Lower Bounds on the Self-Avoiding-Walk Connective Constant - Hara, Slade, al. (1993) (3 citations) Self-citation (Hara) (Correct)
....cos k 2 cos k 3 = 8 : 6s 3 (n = 3) 60s 4 Gamma 180s 5 (n = 5) 630s 5 O(s 6 ) n = 7) O(s 6 ) n 9) A:13) The above, combined with the expansion 1 1 Gamma D = n X m=0 D m D n 1 1 Gamma D (n 0) A:14) and estimates on errors using Lemma B. 1 of [30], i.e. Z [ Gamma ; d d d k (2 ) d j D(k)j m [1 Gamma D(k) n = O(s m=2 ) d 2n; m 0) A:15) leads to expansions for the integrals I n;m (x) Z [ Gamma ; d d d k (2 ) d D(k) m e ik Deltax [1 Gamma D(k) n : A:16) In particular for C 0 (0; x; 1 ....
T. Hara. Mean field critical behaviour for correlation length for percolation in high dimensions. Prob. Th. and Rel. Fields, 86:337--385, (1990).
The Percolation Phase Transition - Alan Bain Trinity (Correct)
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Hara, T. (1990). Mean-field critical behaviour for correlation length for percolation in high dimensions. Probab. Theor. Relat. Fields, 86:337--385.
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