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 Electronic Communications in Probability > Vol. 1 (1996) > Paper 6 open journal systems 


Simulations and Conjectures for Disconnection Exponents

Emily E. Puckette, Occidental College
Wendelin Werner, Université Paris-Sud and IUF


Abstract
Using Monte-Carlo simulations, we estimate numerically disconnection exponents for planar Brownian motions. These simulations tend to confirm conjectures by Duplantier and Mandelbrot.


Full text: PDF

Pages: 49-64

Published on: September 25, 1996


Bibliography
  1. Burdzy, K., Lawler, G.F., Non-intersection exponents for random walk and Brownian motion I. Existance and an invariance principle, Probab. Th. rel. Fields 84, 393-410 (1990) Math. Review 91g:60096
  2. Burdzy, K., Lawler, G.F., Nonintersection exponents for Brownian paths II. Estimates and applications to a random fractal, Ann. Prob. 18, 981-1009 (1990) Math. Review 91g:60097
  3. Burdzy, K., Lawler, G.F., Polaski, T., On the critical exponent for random walk intersections, J. Stat. Phys. 56, 1-12 (1989)
  4. Burdzy, K., Werner, W., No triple point of planar Brownian motion is accessible Ann. Prob. 24, 125-147 (1996)
  5. Cranston, M., Mountford, T., An extension of a result by Burdzy and Lawler, Probab. Th. rel. Fields 89, 487-502 (1991) Math. Review 92k:60155
  6. Duplantier, B., Kwon, H.-H., Conformal invariance and intersection of random walks Phys. Rev. Lett. 61, 2514-2517 (1988)
  7. Duplantier, B., Lawler, G.F., Le Gall, J.F., Lyons, T.J., The geometry of the Brownian curve, in: Probabilités et Analyse stochastique, Tables rondes de St-Chéron Janvier 1992, Bull. Sc. Math. (2) 117, 91-106 (1993) Math. Review 93k:60205
  8. Goddard, P., Olive, D. (Ed.) Kac-Moody and Virasoro algebras, Adv. Series in Math. Phys. vol.3, World Scientific, 1988. Math. Review 89f:17022
  9. Lawler, G.F., Intersections of random walks, Birkhäuser, Boston, 1991. Math. Review 92f:60122
  10. Lawler, G.F., A discrete analog of a theorem of Makarov, Combinatorics, Probability and Computing 2, 181-200 (1993). Math. Review 95c:31004
  11. Lawler, G.F., Hausdorff dimension of cut points for Brownian motion, Electron. J. Probab. 1, paper no.2 (1996).
  12. Lawler, G.F., The dimension of the frontier of planar Brownian motion, (1996), Electron. Comm. Probab. 1, paper no. 5, pp. 29-47 (1996).
  13. Lawler, G.F., Cut times for simple random walk, Duke University preprint 95-04, (1995), DVI file
  14. Lawler, G.F., Non-intersecting Brownian motions, Math. Phys. Electron. J. , Volume 1, paper no. 4 (1995)
  15. Lawler, G.L., Puckette, E.E., The disconnection exponent for simple random walk, Israel Journal Math., to appear.
  16. Li, B., Sokal, A.D., High-precision Monte-Carlo test of the conformal invariance predictions for two-dimensional mutually avoiding walks, J. Stat. Phys. 61, 723-748 (1990)
  17. Mandelbrot, B.B., The fractal geometry of nature, Freeman, New-York, 1982. Math. Review 84h:00021
  18. Werner, W., On Brownian disconnection exponents, Bernoulli 1, 371-380 (1995).
  19. Werner, W., Bounds for disconnection exponents, Electron. Comm. Probab. 1, paper no. 4, pp. 19-28 (1996).
  20. Werner, W., Asymptotic behaviour of disconnection exponents and non-intersection exponents, Probab. Theor. Rel. Fields, to appear.
















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Electronic Communications in Probability. ISSN: 1083-589X