Reflections onBummock: The Lace ArchiveSymposium
نویسندگان
چکیده
منابع مشابه
The Abstract Lace Expansion
LACES DEFINITION. Let P be a finite set of properties. A mapping l that Ž . assigns to any subset S ; P another subset l S is called a lace map if, for all S, G, S , S ; P: 1 2 Ž . Ž . i l S ; S; Ž . Ž . Ž . Ž . ii l S ; G ; S « l G s l S ; Ž . Ž . Ž . Ž . Ž . iii l S s l S « l S j S s l S . 1 2 1 2 1 Ž . Ž . Ž . A set L for which l L s L is called a lace. By applying ii to G s l S , Ž Ž .. Ž ....
متن کاملThe abstract lace expansion
David Brydges and Thomas Spencer's Lace Expansion is abstracted, and it is shown how it sometimes gives rise to sieves. LACES Definition: Let P be a finite set of properties. A mapping l that assigns to any subset S ⊂ P another subset l(S), is called a lace-map, A set L for which l(L) = L is called a lace. By applying (ii) to G = l(S), it is seen that l(l(S)) = l(S), for any set of properties S...
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We give an introduction to the lace expansion for self-avoiding walks, with emphasis on self-avoiding polygons, and with a focus on combinatorial rather than analytical aspects. We derive the lace expansion for self-avoiding walks, and show that this is equivalent to taking the reciprocal of the self-avoiding walk generating function. We list some of the rigorous results for self-avoiding walks...
متن کاملThe Lace Expansion and its Applications
ii The Lace Expansion and its Applications The Lace Expansion and its Applications iii Preface Several superficially simple mathematical models, such as the self-avoiding walk and percolation, are paradigms for the study of critical phenomena in statistical mechanics. Although these models have been studied by mathematicians for about half a century, exciting new developments continue to occur ...
متن کاملLace expansion for the Ising model
The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we prove the lace expansion for the Ising model that is valid for any spin-spin coupling. For the ferromagnetic case, we also prove that the expansion coefficients ...
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ژورنال
عنوان ژورنال: TEXTILE
سال: 2019
ISSN: 1475-9756,1751-8350
DOI: 10.1080/14759756.2019.1648724