Asymptotic expansions in  n  −1  for percolation critical values on the  n ‐Cube and ℤ  n | Zendy

van der Hofstad Remco | Zendy; Slade Gordon | Zendy

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Asymptotic expansions in n −1 for percolation critical values on the n ‐Cube and ℤ n

Author(s) -

van der Hofstad Remco,

Slade Gordon

Publication year - 2005

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.20074

Subject(s) - cube (algebra) , percolation (cognitive psychology) , mathematics , lattice (music) , percolation threshold , combinatorics , asymptotic expansion , k nearest neighbors algorithm , condensed matter physics , statistical physics , physics , mathematical analysis , quantum mechanics , computer science , electrical resistivity and conductivity , neuroscience , artificial intelligence , acoustics , biology

We use the lace expansion to prove that the critical values for nearest‐neighbor bond percolation on the n ‐cube {0, 1} n and on the integer lattice ℤ n have asymptotic expansions, with rational coefficients, to all orders in powers of n −1 . © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005

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