Red Lace Lingerie

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 ....

The 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...

Polygons and the Lace Expansion

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...

Crochet Lace as Expression of Digital Culture

The 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 ...