Exposants critiques pour le mouvement brownien et les marches aléatoires

Jean-François Le Gall

Séminaire Bourbaki (1999-2000)

  • Volume: 42, page 29-51
  • ISSN: 0303-1179

How to cite

top

Le Gall, Jean-François. "Exposants critiques pour le mouvement brownien et les marches aléatoires." Séminaire Bourbaki 42 (1999-2000): 29-51. <http://eudml.org/doc/110278>.

@article{LeGall1999-2000,
author = {Le Gall, Jean-François},
journal = {Séminaire Bourbaki},
keywords = {Brownian; exponent; oriented bridges; random walks with deleted loops; domino pavings; temperlien polyomino},
language = {fre},
pages = {29-51},
publisher = {Société Mathématique de France},
title = {Exposants critiques pour le mouvement brownien et les marches aléatoires},
url = {http://eudml.org/doc/110278},
volume = {42},
year = {1999-2000},
}

TY - JOUR
AU - Le Gall, Jean-François
TI - Exposants critiques pour le mouvement brownien et les marches aléatoires
JO - Séminaire Bourbaki
PY - 1999-2000
PB - Société Mathématique de France
VL - 42
SP - 29
EP - 51
LA - fre
KW - Brownian; exponent; oriented bridges; random walks with deleted loops; domino pavings; temperlien polyomino
UR - http://eudml.org/doc/110278
ER -

References

top
  1. [1] L.V. Ahlfors - Conformal Invariants, Topics in Geometric Function Theory. McGraw-Hill, New York1973 Zbl0272.30012MR357743
  2. [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. Fields84 (1990), 393-410. Zbl0685.60080MR1035664
  3. [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. Zbl0719.60085MR1062056
  4. [4] K. Burdzy, W. Werner - No triple point of planar Brownian motion is accessible. Ann. Probab.24 (1996), 125-147. Zbl0860.60063MR1387629
  5. [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. Zbl0785.60007MR1235419
  6. [6] M. Cranston, T. Mountford - An extension of a result by Burdzy and Lawler. Probab. Th. Rel. Fields89 (1991), 487-502. Zbl0725.60072MR1118560
  7. [7] B. Duplantier - Loop-erased self-avoiding walks in two dimensions : exact critical exponents and winding numbers. PhysicaA191 (1992), 516-522. 
  8. [8] B. Duplantier - Random walks and quantum gravity in two dimensions. Phys. Rev. Lett.81 (1998), 5489-5492. Zbl0949.83056MR1666816
  9. [9] B. Duplantier - Two-dimensional copolymers and exact conformal multifractality. Phys. Rev. Lett.82 (1999), 880-883. MR1688869
  10. [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. Zbl1086.82501MR952941
  11. [11] B. Duplantier, K.-H. Kwon - Conformal invariance and intersections of random walks. Phys. Rev. Lett.61 (1988), 2514-2517. 
  12. [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. Zbl0778.60058MR1205413
  13. [13] P. Kasteleyn - The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice. Physica27 (1961), 1209-1225. Zbl1244.82014
  14. [14] P. Kasteleyn - Graph theory and crystal physics. In : Graph Theory and Theoretical Physics. Academic Press, London1967 Zbl0205.28402MR253689
  15. [15] R. Kenyon - Local statistics of lattice dimers. Ann. Inst. Henri Poincaré Probab. Stat.33 (1997), 591-618. Zbl0893.60047MR1473567
  16. [16] R. Kenyon - Conformal invariance of domino tilings. Preprint. MR1782431
  17. [17] R. Kenyon - The asymptotic determinant of the discrete Laplacian. Preprint. MR1819995
  18. [18] R. Kenyon, J. Propp, D. Wilson - Trees and matchings. Preprint. MR1756162
  19. [19] G.F. Lawler - A self-avoiding random walk. Duke Math. J.47 (1980), 655-693. Zbl0445.60058MR587173
  20. [20] G.F. Lawler - Intersections of Random Walks. Birkhäuser, Boston1991 Zbl0925.60078MR1117680
  21. [21] G.F. Lawler - Hausdorff dimension of cut points for Brownian motion. Electron. J. Probab.1 (1996), no 2. Zbl0891.60078MR1386294
  22. [22] G.F. Lawler - The dimension of the frontier of planar Brownian motion. Electronic Commm. Probab.1 (1996), no 5. Zbl0857.60083MR1386294
  23. [23] G.F. Lawler - Loop-erased random walk. In : Perplexing Problems in Probability. Birkhäuser, Boston1999 Zbl0947.60055MR1703133
  24. [24] G.F. Lawler, W. Werner - Intersection exponents for planar Brownian motion. Preprint. MR1742883
  25. [25] G.F. Lawler, W. Werner - Universality for conformally invariant intersection exponents. Preprint. MR1796962
  26. [26] G.F. Lawler, O. Schramm, W. Werner - Values of Brownian intersection exponents I : Half-plane exponents. Preprint. Zbl1005.60097MR1879850
  27. [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. [28] B.B. Mandelbrot - The Fractal Geometry of Nature. Freeman 1982. Zbl0504.28001MR665254
  29. [29] R. Pemantle - Choosing a spanning tree for the integer lattice uniformly. Ann. Probab.19 (1991), 1559-1574. Zbl0758.60010MR1127715
  30. [30] O. Schramm - Scaling limits of loop-erased random walks and uniform spanning trees. Preprint. MR1776084
  31. [31] H. Temperley - Combinatorics : Proceedings of the British Combinatorial Conference 1973. LondonMath. Soc. Lecture Notes Series13 (1974), 202-204. Zbl0453.00011MR345829
  32. [32] H. Temperley, M. Fisher - The dimer problem in statistical mechanics - an exact result. Phil. Mag.6 (1961), 1061-1063. Zbl0126.25102MR136398
  33. [33] W. Werner - Asymptotic behaviour of disconnection and intersection exponents. Probab. Th. Rel. Fields108 (1997), 131-152. Zbl0876.60065MR1452553

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.