Exposants critiques pour le mouvement brownien et les marches aléatoires

Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque no. 276 (2002), Talk no. 866, p. 29-51

@incollection{SB_1999-2000__42__29_0,
     author = {Le Gall, Jean-Fran\c cois},
     title = {Exposants critiques pour le mouvement brownien et les marches al\'eatoires},
     booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {276},
     year = {2002},
     note = {talk:866},
     pages = {29-51},
     zbl = {1012.60072},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1999-2000__42__29_0}
}

Le Gall, Jean-François. Exposants critiques pour le mouvement brownien et les marches aléatoires, in Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Talk no. 866, pp. 29-51. http://www.numdam.org/item/SB_1999-2000__42__29_0/

References

[1] L. V. Ahlfors - Conformal Invariants, Topics in Geometric Function Theory. McGraw-Hill, New York 1973 | MR 357743 | Zbl 0272.30012

[2] K. Burdzy, G. F. Lawler - Non-intersection exponents for random walk and Brownian motion. Part I : Existence and an invariance principle. Probab. Th. Rel. Fields 84 (1990), 393-410. | MR 1035664 | Zbl 0685.60080

[3] K. Burdzy, G. F. Lawler - Non-intersection exponents for random walk and Brownian motion. Part II : Estimates and applications to a random fractal. Ann. Probab. 18 (1990), 981-1009. | MR 1062056 | Zbl 0719.60085

[4] K. Burdzy, W. Werner - No triple point of planar Brownian motion is accessible. Ann. Probab. 24 (1996), 125-147. | MR 1387629 | Zbl 0860.60063

[5] R. Burton, R. Pemantle - Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer impedances. Ann. Probab. 21 (1993), 1329-1371. | MR 1235419 | Zbl 0785.60007

[6] M. Cranston, T. Mountford - An extension of a result by Burdzy and Lawler. Probab. Th. Rel. Fields 89 (1991), 487-502. | MR 1118560 | Zbl 0725.60072

[7] B. Duplantier - Loop-erased self-avoiding walks in two dimensions : exact critical exponents and winding numbers. Physica A 191 (1992), 516-522.

[8] B. Duplantier - Random walks and quantum gravity in two dimensions. Phys. Rev. Lett. 81 (1998), 5489-5492. | MR 1666816 | Zbl 0949.83056

[9] B. Duplantier - Two-dimensional copolymers and exact conformal multifractality. Phys. Rev. Lett. 82 (1999), 880-883. | MR 1688869

[10] B. Duplantier, F. David - Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice. J. Stat. Phys. 51 (1988), 327-434. | MR 952941 | Zbl 1086.82501

[11] B. Duplantier, K.-H. Kwon - Conformal invariance and intersections of random walks. Phys. Rev. Lett. 61 (1988), 2514-2517.

[12] B. Duplantier, G. F. Lawler, J. F. Le Gall, T. J. Lyons - The geometry of the Brownian curve. Bull. Sci. math. 117 (1993), 91-106. | MR 1205413 | Zbl 0778.60058

[13] P. Kasteleyn - The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice. Physica 27 (1961), 1209-1225.

[14] P. Kasteleyn - Graph theory and crystal physics. In : Graph Theory and Theoretical Physics. Academic Press, London 1967 | MR 253689 | Zbl 0205.28402

[15] R. Kenyon - Local statistics of lattice dimers. Ann. Inst. Henri Poincaré Probab. Stat. 33 (1997), 591-618. | Numdam | MR 1473567 | Zbl 0893.60047

[16] R. Kenyon - Conformal invariance of domino tilings. Preprint. | MR 1782431

[17] R. Kenyon - The asymptotic determinant of the discrete Laplacian. Preprint. | MR 1819995

[18] R. Kenyon, J. Propp, D. Wilson - Trees and matchings. Preprint. | MR 1756162

[19] G. F. Lawler - A self-avoiding random walk. Duke Math. J. 47 (1980), 655-693. | MR 587173 | Zbl 0445.60058

[20] G. F. Lawler - Intersections of Random Walks. Birkhäuser, Boston 1991 | MR 1117680 | Zbl 0925.60078

[21] G. F. Lawler - Hausdorff dimension of cut points for Brownian motion. Electron. J. Probab. 1 (1996), no 2. | MR 1386294 | Zbl 0891.60078

[22] G. F. Lawler - The dimension of the frontier of planar Brownian motion. Electronic Commm. Probab. 1 (1996), no 5. | MR 1386294 | Zbl 0857.60083

[23] G. F. Lawler - Loop-erased random walk. In : Perplexing Problems in Probability. Birkhäuser, Boston 1999 | MR 1703133 | Zbl 0947.60055

[24] G. F. Lawler, W. Werner - Intersection exponents for planar Brownian motion. Preprint. | MR 1742883

[25] G. F. Lawler, W. Werner - Universality for conformally invariant intersection exponents. Preprint. | MR 1796962

[26] G. F. Lawler, O. Schramm, W. Werner - Values of Brownian intersection exponents I : Half-plane exponents. Preprint. | MR 1879850

[27] S. N. Majumdar - Exact fractal dimension of the loop-erased self-avoiding walk in two dimensions. Phys. Rev. Lett. 68 (1992), 2329-2331.

[28] B. B. Mandelbrot - The Fractal Geometry of Nature. Freeman 1982. | MR 665254 | Zbl 0504.28001

[29] R. Pemantle - Choosing a spanning tree for the integer lattice uniformly. Ann. Probab. 19 (1991), 1559-1574. | MR 1127715 | Zbl 0758.60010

[30] O. Schramm - Scaling limits of loop-erased random walks and uniform spanning trees. Preprint. | MR 1776084

[31] H. Temperley - Combinatorics : Proceedings of the British Combinatorial Conference 1973. London Math. Soc. Lecture Notes Series 13 (1974), 202-204. | MR 345829 | Zbl 0453.00011

[32] H. Temperley, M. Fisher - The dimer problem in statistical mechanics - an exact result. Phil. Mag. 6 (1961), 1061-1063. | MR 136398 | Zbl 0126.25102

[33] W. Werner - Asymptotic behaviour of disconnection and intersection exponents. Probab. Th. Rel. Fields 108 (1997), 131-152. | MR 1452553 | Zbl 0876.60065