Diagrammatic Estimates for the Lace Expansion

2017 ◽  
pp. 77-99
Author(s):  
Markus Heydenreich ◽  
Remco van der Hofstad
Keyword(s):  
Lace Expansion

Self-avoiding walk enumeration via the lace expansion

2007 ◽  
Vol 40 (36) ◽  
pp. 10973-11017 ◽  
Author(s):  
Nathan Clisby ◽  
Richard Liang ◽  
Gordon Slade
Keyword(s):  
Lace Expansion ◽  
Self Avoiding Walk

scholarly journals Generalized approach to the non-backtracking lace expansion

2016 ◽  
Vol 169 (3-4) ◽  
pp. 1041-1119 ◽  
Author(s):  
Robert Fitzner ◽  
Remco van der Hofstad
Keyword(s):  
Lace Expansion

scholarly journals Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models

2003 ◽  
Vol 31 (1) ◽  
pp. 349-408 ◽  
Author(s):  
Takashi Hara ◽  
Remco van der Hofstad ◽  
Gordon Slade
Keyword(s):  
High Dimensional ◽  
Lace Expansion

scholarly journals Critical Site Percolation in High Dimension

2020 ◽  
Vol 181 (3) ◽  
pp. 816-853
Author(s):  
Markus Heydenreich ◽  
Kilian Matzke
Keyword(s):  
High Dimension ◽  
Critical Exponents ◽  
Mean Field ◽  
High Dimensions ◽  
Lace Expansion ◽  
Site Percolation ◽  
Triangle Condition ◽  
Hypercubic Lattice ◽  
Infra Red ◽  
Critical Site

Abstract We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.

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