44 citations · 136 across the 24 of their papers we have counts for
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math.PR2007★ 44 cited
Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk
Markus Heydenreich, Remco van der Hofstad, Akira Sakai
We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if $d>2(α\w…
math.PR2007★ 6 cited
Diagrammatic bounds on the lace-expansion coefficients for oriented percolation
Akira Sakai
We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical b…
math.PR2007
Critical behavior and the limit distribution for long-range oriented percolation. I
Lung-Chi Chen, Akira Sakai
We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Sup…