메뉴 건너뛰기




Volumn 116, Issue 1-4, 2004, Pages 157-173

Continuum nonsimple loops and 2D critical percolation

Author keywords

conformal invariance; continuum loops; nonsimple loops; percolation; scaling limit; SLE; triangular lattice

Indexed keywords


EID: 4344576881     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOSS.0000037221.31328.75     Document Type: Article
Times cited : (29)

References (30)
  • 3
    • 0000614574 scopus 로고    scopus 로고
    • Scaling limits of loop-erased random walks and uniform spanning trees
    • O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees, Israel J. Math. 118:221-288 (2000).
    • (2000) Israel J. Math. , vol.118 , pp. 221-288
    • Schramm, O.1
  • 4
    • 0041869040 scopus 로고    scopus 로고
    • Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits
    • S. Smirnov, Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits, C. R. Acad. Sci. Paris 333:239-244 (2001).
    • (2001) C. R. Acad. Sci. Paris , vol.333 , pp. 239-244
    • Smirnov, S.1
  • 5
    • 0012566413 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents I: Half-plane exponents
    • G. Lawler, O. Schramm, and W. Werner, Values of Brownian intersection exponents I: Half-plane exponents, Acta Math. 187:237-273 (2001).
    • (2001) Acta Math. , vol.187 , pp. 237-273
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 6
    • 0000467140 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents II: Plane exponents
    • G. Lawler, O. Schramm, and W. Werner, Values of Brownian intersection exponents II: Plane exponents, Acta Math. 187:275-308 (2001).
    • (2001) Acta Math. , vol.187 , pp. 275-308
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 7
    • 1342292650 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents III: Two-sided exponents
    • G. Lawler, O. Schramm, and W. Werner, Values of Brownian intersection exponents III: Two-sided exponents, Ann. Inst. Henri Poincaré 38:109-123 (2002).
    • (2002) Ann. Inst. Henri Poincaré , vol.38 , pp. 109-123
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 8
    • 0036948020 scopus 로고    scopus 로고
    • Analyticity of intersection exponents for planar Brownian motion
    • G. Lawler, O. Schramm, and W. Werner, Analyticity of intersection exponents for planar Brownian motion, Acta Math. 189:179-201 (2002).
    • (2002) Acta Math. , vol.189 , pp. 179-201
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 10
    • 0141542070 scopus 로고    scopus 로고
    • Conformal invariance of planar loop-erased random walk and uniform spanning trees
    • to appear, preprint arXiv: math.PR/0112234
    • G. Lawler, O. Schramm, and W. Werner, Conformal invariance of planar loop-erased random walk and uniform spanning trees, Ann. Prob., to appear, preprint arXiv: math.PR/0112234 (2003).
    • (2003) Ann. Prob.
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 11
    • 0141680586 scopus 로고    scopus 로고
    • Conformal restriction: The chordal case
    • arXiv:math.PR/0209343
    • G. Lawler, O. Schramm, and W. Werner, Conformal restriction: The chordal case, J. Amer. Math. Soc., arXiv:math.PR/0209343 16:417-955 (2003).
    • (2003) J. Amer. Math. Soc. , vol.16 , pp. 417-955
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 12
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • S. Smirnov and W. Werner, Critical exponents for two-dimensional percolation, Math. Rev. Lett. 8:729-744 (2001).
    • (2001) Math. Rev. Lett. , vol.8 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 13
    • 85204069219 scopus 로고    scopus 로고
    • Lecture notes for the ICTP School of Probability
    • G. Lawler, Conformally Invariant Processes, Lecture notes for the ICTP School of Probability (2002).
    • (2002) Conformally Invariant Processes
    • Lawler, G.1
  • 14
    • 0037835311 scopus 로고    scopus 로고
    • Lecture notes from the 2002 Saint-Flour summer school (Springer), to appear, preprint arXiv: math.PR/0204277.
    • W. Werner, Random Planar Curves and Schramm-Loewner Evolutions, Lecture notes from the 2002 Saint-Flour summer school (Springer, 2003), to appear, preprint arXiv: math.PR/0204277.
    • (2003) Random Planar Curves and Schramm-Loewner Evolutions
    • Werner, W.1
  • 16
    • 0001056718 scopus 로고    scopus 로고
    • Hölder regularity and dimension bounds for random curves
    • M. Aizenman and A. Burchard, Hölder regularity and dimension bounds for random curves, Duke Math. J. 99:419-453 (1999).
    • (1999) Duke Math. J. , vol.99 , pp. 419-453
    • Aizenman, M.1    Burchard, A.2
  • 17
    • 0033415760 scopus 로고    scopus 로고
    • Scaling limits for minimal and random spanning trees in two dimensions
    • M. Aizenman, A. Burchard, C. M. Newman, and D. B. Wilson, Scaling limits for minimal and random spanning trees in two dimensions, Ran. Structures Alg. 15:316-367 (1999).
    • (1999) Ran. Structures Alg. , vol.15 , pp. 316-367
    • Aizenman, M.1    Burchard, A.2    Newman, C.M.3    Wilson, D.B.4
  • 19
    • 2142651448 scopus 로고    scopus 로고
    • A particular bit of universality: Scaling limits of some dependent percolation models
    • to appear
    • F. Camia, C. M. Newman, and V. Sidoravicius, A particular bit of universality: Scaling limits of some dependent percolation models, Comm. Math. Phys., to appear (2004).
    • (2004) Comm. Math. Phys.
    • Camia, F.1    Newman, C.M.2    Sidoravicius, V.3
  • 20
    • 0007122531 scopus 로고    scopus 로고
    • Almost all words are seen in critical site percolation on the triangular lattice
    • H. Kesten, V. Sidoravicius, and Y. Zhang, Almost all words are seen in critical site percolation on the triangular lattice, Electr. J. Probab. 3 (1998), 10 pp.
    • (1998) Electr. J. Probab. , vol.3 , pp. 10
    • Kesten, H.1    Sidoravicius, V.2    Zhang, Y.3
  • 21
    • 0000578291 scopus 로고
    • Structure and perimeters of percolation clusters
    • T. Grossman and A. Aharony, Structure and perimeters of percolation clusters, J. Phys. A 19:L745-L751 (1986).
    • (1986) J. Phys. A , vol.19
    • Grossman, T.1    Aharony, A.2
  • 22
    • 36149032174 scopus 로고
    • Accessible external perimeter of percolation clusters
    • T. Grossman and A. Aharony, Accessible external perimeter of percolation clusters, J. Phys. A 20:L1193-L1201 (1987).
    • (1987) J. Phys. A , vol.20
    • Grossman, T.1    Aharony, A.2
  • 23
    • 0000360856 scopus 로고    scopus 로고
    • Connectivity exponents and the external perimeter in 2D independent percolation
    • M. Aizenman, B. Duplantier, and A. Aharony, Connectivity exponents and the external perimeter in 2D independent percolation, Phys. Rev. Lett. 83:1359-1362 (1999).
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 1359-1362
    • Aizenman, M.1    Duplantier, B.2    Aharony, A.3
  • 24
    • 0000898051 scopus 로고
    • Critical percolation in finite geometries
    • J. L. Cardy, Critical percolation in finite geometries, J. Phys. A 25:L201-L206 (1992).
    • (1992) J. Phys. A , vol.25
    • Cardy, J.L.1
  • 26
    • 0242371637 scopus 로고    scopus 로고
    • Basic properties of SLE
    • to appear, preprint arXiv:math.PR0106036
    • S. Rohde and O. Schramm, Basic properties of SLE, Ann. Math., to appear, preprint arXiv:math.PR0106036 (2003).
    • (2003) Ann. Math.
    • Rohde, S.1    Schramm, O.2
  • 27
    • 0141430358 scopus 로고    scopus 로고
    • Critical exponents, conformal invariance and planar Brownian motion, in
    • W. Werner, Critical exponents, conformal invariance and planar Brownian motion, in Proceedings of the 3rd Europ. Congress of Math., Prog. Math., Vol. 202 (2001), pp. 87-103.
    • (2001) Proceedings of the 3rd Europ. Congress of Math., Prog. Math. , vol.202 , pp. 87-103
    • Werner, W.1
  • 28
    • 0000493287 scopus 로고    scopus 로고
    • Universality for conformally invariant intersection exponents
    • G. Lawler and W. Werner, Universality for conformally invariant intersection exponents, J. Eur. Math. Soc. 2:291-328 (2000).
    • (2000) J. Eur. Math. Soc. , vol.2 , pp. 291-328
    • Lawler, G.1    Werner, W.2
  • 29
    • 34250275869 scopus 로고
    • A note on percolation
    • L. Russo, A note on percolation, Z. Wahrsch. Ver. Geb. 43:39-48 (1978).
    • (1978) Z. Wahrsch. Ver. Geb. , vol.43 , pp. 39-48
    • Russo, L.1
  • 30
    • 77957093986 scopus 로고
    • Percolation probabilities on the square lattice
    • Annals of Discrete Mathematics, B. Bollobás, ed. North-Holland, Amsterdam
    • P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, in Advances in Graph Theory, Annals of Discrete Mathematics, Vol. 3, B. Bollobás, ed. (North-Holland, Amsterdam, 1978), pp. 227-245.
    • (1978) Advances in Graph Theory , vol.3 , pp. 227-245
    • Seymour, P.D.1    Welsh, D.J.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.