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Download Communications in Mathematical Physics - Volume 186 by A. Jaffe (Chief Editor) PDF

By A. Jaffe (Chief Editor)

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GolinelS, E. Guitter with the same value of u = 1. 79) leads to a wrong result for the meander determinant, D~(2), for large n. 19) for the large n asymptotics of log det D~ (0)). 81). This simply means that the configurations of a C 1 ~ dominating the meander determinant are very different from those dominating the trace of the Gram matrix or the (semi-)meander polynomial. q > 2 . 71), with q = e ~ + c - ~ 0 > 0. 71) is dominated by large g's for large n. ~i=o , ~ + 1 - ~ . . 68). This gives an asymptotic sum rule involving the f~,b'S and q.

1). 17) 58 P. Di Francesco, O. Golinelli, E. 14) for k = 2p + 1. 20). 14) for k = 2p. Acknowledgement. We thank A. [4] to our knowledge, R. Balian for helpful discussions, S. -B. Zuber for a careful reading of the manuscript. Meanders and the Temperley-Lieb Algebra 59 References 1. : Sorting Jordan sequences in linear time using level-linked search trees. Information and Control 68, 170-184 (1986) 2. : La topologia dei labirinti. In M. Emmet, ed. L' occhio di Horus: Itinerario nell'immaginario matematico, Istituto della Enciclopedia Italia, Roma, 1989 pp.

T, the corresponding portions of b, and elevating the interior portion by shifting the ga's of p ! - l ) by +1, and adding g~ = g~j+2 = 0. 7) j--o (k) , More generally, the same reasoning applies to r/n+1 with the result (see Fig. 8) ) "n--j, j---0 where two situations may now occur for the part of a corresponding to the interior of the arch: either g~ = g2~+l = 1, in which case the restriction condition on a is lowered by 1 (term r/~k+l)), or g~ = gEaj+l --- --1, which may occur as soon as k >_ 1, in which case the restriction condition is raised by 1 (term r/~k-1)).

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