메뉴 건너뛰기




Volumn 27, Issue 4, 1999, Pages 1601-1642

Intersection exponents for planar Brownian motion

Author keywords

Brownian motion; Conformal invariance; Critical exponents

Indexed keywords


EID: 0033233660     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022874810     Document Type: Article
Times cited : (43)

References (35)
  • 2
    • 0001056718 scopus 로고    scopus 로고
    • Hölder regularity and dimension bounds for random curves
    • AIZENMAN, M. and BURCHARD, A. (1999). Hölder regularity and dimension bounds for random curves. Duke Math. J. 99 419-453.
    • (1999) Duke Math. J. , vol.99 , pp. 419-453
    • Aizenman, M.1    Burchard, A.2
  • 4
    • 0009453792 scopus 로고
    • Non-intersection exponents for random walk and Brownian motion I: Existence and an invariance principle
    • BURDZY, K. and LAWLER, G. F. (1990). Non-intersection exponents for random walk and Brownian motion I: Existence and an invariance principle. Probab. Theory Related Fields 84 393-410.
    • (1990) Probab. Theory Related Fields , vol.84 , pp. 393-410
    • Burdzy, K.1    Lawler, G.F.2
  • 5
    • 0000557204 scopus 로고
    • Non-intersection exponents for random walk and Brownian motion II: Estimates and applications to a random fractal
    • BURDZY, K. and LAWLER, G. F. (1990). Non-intersection exponents for random walk and Brownian motion II: Estimates and applications to a random fractal. Ann. Probab. 18 981-1009.
    • (1990) Ann. Probab. , vol.18 , pp. 981-1009
    • Burdzy, K.1    Lawler, G.F.2
  • 6
    • 0009400513 scopus 로고
    • On the critical exponent for random walk intersections
    • BURDZY, K., LAWLER, G. F. and POLASKI, T. (1989). On the critical exponent for random walk intersections. J. Statist. Phys. 56 1-12.
    • (1989) J. Statist. Phys. , vol.56 , pp. 1-12
    • Burdzy, K.1    Lawler, G.F.2
  • 7
    • 0030501795 scopus 로고    scopus 로고
    • No triple point of planar Brownian motion is accessible
    • BURDZY, K. and WERNER, W. (1996). No triple point of planar Brownian motion is accessible. Ann. Probab. 24 125-147.
    • (1996) Ann. Probab. , vol.24 , pp. 125-147
    • Burdzy, K.1    Werner, W.2
  • 9
    • 0000113134 scopus 로고
    • Loop-erased self-avoiding walks in two dimensions: Exact critical exponents and winding numbers
    • DUPLANTIER, B. (1992). Loop-erased self-avoiding walks in two dimensions: exact critical exponents and winding numbers. Phys. A 191 516-522.
    • (1992) Phys. A , vol.191 , pp. 516-522
    • Duplantier, B.1
  • 10
    • 0002877490 scopus 로고
    • Conformal invariance and intersection of random walks
    • DUPLANTIER, B. and KWON, K.-H. (1988). Conformal invariance and intersection of random walks. Phys. Rev. Lett. 61 2514-2517.
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2514-2517
    • Duplantier, B.1    Kwon, K.-H.2
  • 16
    • 84971723033 scopus 로고
    • A discrete analogue of a theorem of Makarov
    • LAWLER, G. F. (1993). A discrete analogue of a theorem of Makarov. Combin. Probab. Comput. 2 181-200.
    • (1993) Combin. Probab. Comput. , vol.2 , pp. 181-200
    • Lawler, G.F.1
  • 17
    • 3042574952 scopus 로고
    • Hausdorff dimension of cut points for Brownian motion
    • LAWLER, G. F. (1995). Hausdorff dimension of cut points for Brownian motion. Electron. J. Probab. 1 1-20.
    • (1995) Electron. J. Probab. , vol.1 , pp. 1-20
    • Lawler, G.F.1
  • 18
    • 0003257551 scopus 로고    scopus 로고
    • The dimension of the frontier of planar Brownian motion
    • LAWLER, G. F. (1996). The dimension of the frontier of planar Brownian motion. Electron. Comm. Probab. 1 29-47.
    • (1996) Electron. Comm. Probab. , vol.1 , pp. 29-47
    • Lawler, G.F.1
  • 19
    • 0039213043 scopus 로고    scopus 로고
    • Cut times for simple random walk
    • LAWLER, G. F. (1997). Cut times for simple random walk. Electron. J. Probab. 1 1-24.
    • (1997) Electron. J. Probab. , vol.1 , pp. 1-24
    • Lawler, G.F.1
  • 21
    • 0007135322 scopus 로고    scopus 로고
    • Strict concavity of the intersection exponent for Brownian motion in two and three dimensions
    • LAWLER, G. F. (1998). Strict concavity of the intersection exponent for Brownian motion in two and three dimensions. Math. Phys. Electron. J. 4 1-67.
    • (1998) Math. Phys. Electron. J. , vol.4 , pp. 1-67
    • Lawler, G.F.1
  • 23
    • 0009434148 scopus 로고    scopus 로고
    • The disconnection exponent for simple random walk
    • LAWLER, G. F. and PUCKETTE, E. E. (1997). The disconnection exponent for simple random walk. Israel J. Math. 99 109-122.
    • (1997) Israel J. Math. , vol.99 , pp. 109-122
    • Lawler, G.F.1    Puckette, E.E.2
  • 25
    • 0009452583 scopus 로고
    • High-precision Monte Carlo test of the conformal invariance predictions for two-dimensional mutually avoiding walks
    • LI, B. and SOKAL, A. D. (1990). High-precision Monte Carlo test of the conformal invariance predictions for two-dimensional mutually avoiding walks. J. Statist. Phys. 61 723-748.
    • (1990) J. Statist. Phys. , vol.61 , pp. 723-748
    • Li, B.1    Sokal, A.D.2
  • 26
    • 84959830189 scopus 로고
    • Distortion of boundary sets under conformal mapping
    • MAKAROV, N. G. (1985). Distortion of boundary sets under conformal mapping. Proc. London Math. Soc. 51 369-384.
    • (1985) Proc. London Math. Soc. , vol.51 , pp. 369-384
    • Makarov, N.G.1
  • 29
    • 0009388113 scopus 로고    scopus 로고
    • Monte-Carlo tests and conjectures for disconnection exponents
    • PUCKETTE, E. E. and WERNER, W. (1996). Monte-Carlo tests and conjectures for disconnection exponents. Electron. Comm. Probab. 1 49-64.
    • (1996) Electron. Comm. Probab. , vol.1 , pp. 49-64
    • Puckette, E.E.1    Werner, W.2
  • 31
    • 0009425343 scopus 로고    scopus 로고
    • Scaling limits of loop-erased random walks and uniform spanning trees
    • To appear
    • SCHRAMM, O. (1999). Scaling limits of loop-erased random walks and uniform spanning trees Israel J. Math. To appear.
    • (1999) Israel J. Math.
    • Schramm, O.1
  • 32
    • 84972537132 scopus 로고
    • On Brownian disconnection exponents
    • WERNER, W. (1995). On Brownian disconnection exponents. Bernoulli 1 371-380.
    • (1995) Bernoulli , vol.1 , pp. 371-380
    • Werner, W.1
  • 33
    • 0002122939 scopus 로고    scopus 로고
    • Bounds for disconnection exponents
    • WERNER, W. (1996). Bounds for disconnection exponents. Electron. Comm. Probab. 1 19-28.
    • (1996) Electron. Comm. Probab. , vol.1 , pp. 19-28
    • Werner, W.1
  • 34
    • 0031138716 scopus 로고    scopus 로고
    • Asymptotic behaviour of disconnection and nonintersection exponents
    • WERNER, W. (1997). Asymptotic behaviour of disconnection and nonintersection exponents. Probab. Theory Related Fields 108 131-152.
    • (1997) Probab. Theory Related Fields , vol.108 , pp. 131-152
    • Werner, W.1
  • 35
    • 0029711422 scopus 로고    scopus 로고
    • Generating random trees more quickly than the cover time
    • WILSON, D. B. (1996). Generating random trees more quickly than the cover time. ACM Symp. Theory of Computing 296-303.
    • (1996) ACM Symp. Theory of Computing , pp. 296-303
    • Wilson, D.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.