메뉴 건너뛰기




Volumn 16, Issue 4, 2003, Pages 917-955

Conformal restriction: The chordal case

Author keywords

Conformal invariance; Random fractals; Restriction property; SLE

Indexed keywords


EID: 0141680586     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-03-00430-2     Document Type: Article
Times cited : (253)

References (51)
  • 2
    • 0037026306 scopus 로고    scopus 로고
    • k, growth processes and conformal field theories
    • k, growth processes and conformal field theories, Phys. Lett. B 543, 135-138.
    • (2002) Phys. Lett. B , vol.543 , pp. 135-138
    • Bauer, M.1    Bernard, D.2
  • 4
    • 0141542072 scopus 로고    scopus 로고
    • arXiv:math.PR/0204208
    • 6, arXiv:math.PR/0204208.
    • (2002) 6
    • Beffara, V.1
  • 5
    • 0004542587 scopus 로고
    • Infinite conformal symmetry of critical fluctuations in two dimensions
    • MR 86e:82019
    • A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov (1984), Infinite conformal symmetry of critical fluctuations in two dimensions, J. Statist. Phys. 34, 763-774. MR 86e:82019
    • (1984) J. Statist. Phys. , vol.34 , pp. 763-774
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 6
    • 0010882054 scopus 로고
    • Infinite conformal symmetry in two-dimensional quantum field theory
    • MR 86m:81097
    • A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov (1984), Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Phys. B 241, 333-380. MR 86m:81097
    • (1984) Nuclear Phys. B , vol.241 , pp. 333-380
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 8
    • 0003456233 scopus 로고
    • Multidimensional Brownian Excursions and Potential Theory
    • John Wiley & Sons. MR 89d:60146
    • K. Burdzy (1987), Multidimensional Brownian Excursions and Potential Theory, Pitman Research Notes in Mathematics 164, John Wiley & Sons. MR 89d:60146
    • (1987) Pitman Research Notes in Mathematics , vol.164
    • Burdzy, K.1
  • 9
    • 0000254242 scopus 로고
    • Conformal invariance and surface critical behavior
    • J.L. Cardy (1984), Conformal invariance and surface critical behavior, Nucl. Phys. B240 (FS12), 514-532.
    • (1984) Nucl. Phys. , vol.B240 , Issue.FS12 , pp. 514-532
    • Cardy, J.L.1
  • 10
    • 0000898051 scopus 로고
    • Critical percolation in finite geometries
    • MR 92m:82048
    • J.L. Cardy (1992), Critical percolation in finite geometries, J. Phys. A, 25 L201-L206. MR 92m:82048
    • (1992) J. Phys. A , vol.25
    • Cardy, J.L.1
  • 14
    • 0001322465 scopus 로고    scopus 로고
    • Random walks and quantum gravity in two dimensions
    • MR 99j:83034
    • B. Duplantier (1998), Random walks and quantum gravity in two dimensions, Phys. Rev. Lett. 81, 5489-5492. MR 99j:83034
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5489-5492
    • Duplantier, B.1
  • 15
    • 0002877490 scopus 로고
    • Conformal invariance and intersection of random walks
    • B. Duplantier, K.-H. Kwon (1988), Conformal invariance and intersection of random walks, Phys. Rev. Let. 61, 2514-2517.
    • (1988) Phys. Rev. Let. , vol.61 , pp. 2514-2517
    • Duplantier, B.1    Kwon, K.-H.2
  • 16
    • 0001024607 scopus 로고
    • Exact surface and wedge exponents for polymers in two dimensions
    • MR 88e:82022
    • B. Duplantier, H. Saleur (1986), Exact surface and wedge exponents for polymers in two dimensions, Phys. Rev. Lett. 57, 3179-3182. MR 88e:82022
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 3179-3182
    • Duplantier, B.1    Saleur, H.2
  • 18
    • 0038391346 scopus 로고    scopus 로고
    • Conformal fields, restriction properties, degenerate representations and SLE
    • R. Friedrich, W. Werner (2002), Conformal fields, restriction properties, degenerate representations and SLE, C.R. Ac. Sci. Paris Ser. I Math 335, 947-952.
    • (2002) C.R. Ac. Sci. Paris Ser. I Math , vol.335 , pp. 947-952
    • Friedrich, R.1    Werner, W.2
  • 20
    • 0141560572 scopus 로고    scopus 로고
    • A faster implementation of the pivot algorithm for self-avoiding walks
    • T. Kennedy (2002), A faster implementation of the pivot algorithm for self-avoiding walks, J. Stat. Phys. 106, 407-429.
    • (2002) J. Stat. Phys. , vol.106 , pp. 407-429
    • Kennedy, T.1
  • 21
    • 0036536611 scopus 로고    scopus 로고
    • Monte Carlo tests of SLE predictions for the 2D self-avoiding walk
    • T. Kennedy (2002), Monte Carlo tests of SLE predictions for the 2D self-avoiding walk, Phys. Rev. Lett. 88, 130601.
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 130601
    • Kennedy, T.1
  • 23
    • 0012566413 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents I: Half-plane exponents
    • MR 2002m:60159a
    • G.F. Lawler, O. Schramm, W. Werner (2001), Values of Brownian intersection exponents I: Half-plane exponents. Acta Mathematica 187, 237-273. MR 2002m:60159a
    • (2001) Acta Mathematica , vol.187 , pp. 237-273
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 24
    • 0000467140 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents II: Plane exponents
    • MR 2002m:60159b
    • G.F. Lawler, O. Schramm, W. Werner (2001), Values of Brownian intersection exponents II: Plane exponents. Acta Mathematica 187, 275-308. MR 2002m:60159b
    • (2001) Acta Mathematica , vol.187 , pp. 275-308
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 25
    • 1342292650 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents III: Two-sided exponents
    • MR 2003d:60163
    • G.F. Lawler, O. Schramm, W. Werner (2002), Values of Brownian intersection exponents III: Two-sided exponents. Ann. Inst. Henri Poincaré 38, 109-123. MR 2003d:60163
    • (2002) Ann. Inst. Henri Poincaré , vol.38 , pp. 109-123
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 26
    • 0036948020 scopus 로고    scopus 로고
    • Analyticity of planar Brownian intersection exponents
    • G.F. Lawler, O. Schramm, W. Werner (2002), Analyticity of planar Brownian intersection exponents. Acta Mathematica 189, 179-201.
    • (2002) Acta Mathematica , vol.189 , pp. 179-201
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 27
    • 0344939384 scopus 로고    scopus 로고
    • Sharp estimates for Brownian non-intersection probabilities
    • V. Sidoravicius, Ed., Prog. Probab., Birkhauser. MR 2003d:60162
    • G.F. Lawler, O. Schramm, W. Werner (2001), Sharp estimates for Brownian non-intersection probabilities, in In and Out of Equilbrium, V. Sidoravicius, Ed., Prog. Probab., Birkhauser, 113-131. MR 2003d:60162
    • (2001) In and Out of Equilbrium , pp. 113-131
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 28
    • 0242384526 scopus 로고    scopus 로고
    • One-arm exponent for critical 2D percolation
    • paper no. 2. MR 2002k:60204
    • G.F. Lawler, O. Schramm, W. Werner (2002), One-arm exponent for critical 2D percolation, Electronic J. Probab. 7, paper no. 2. MR 2002k:60204
    • (2002) Electronic J. Probab. , vol.7
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 29
    • 0141542070 scopus 로고    scopus 로고
    • Conformal invariance of planar loop-erased random walks and uniform spanning trees
    • arXiv:math.PR/0112234, to appear
    • G.F. Lawler, O. Schramm, W. Werner (2001), Conformal invariance of planar loop-erased random walks and uniform spanning trees, arXiv:math.PR/0112234, Ann. Prob., to appear.
    • (2001) Ann. Prob.
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 30
    • 33646495504 scopus 로고    scopus 로고
    • On the scaling limit of planar self-avoiding walks
    • math.PR/0204277, Fractal geometry and application, A jubilee of Benoit Mandelbrot, to appear
    • G.F. Lawler, O. Schramm, W. Werner (2002), On the scaling limit of planar self-avoiding walks, math.PR/0204277, in Fractal geometry and application, A jubilee of Benoit Mandelbrot, AMS Proc. Symp. Pure Math., to appear.
    • (2002) AMS Proc. Symp. Pure Math.
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 32
    • 0000493287 scopus 로고    scopus 로고
    • Universality for conformally invariant intersection exponents
    • MR 2002g:60123
    • G.F. Lawler, W. Werner (2000), Universality for conformally invariant intersection exponents, J. Europ. Math. Soc. 2, 291-328. MR 2002g:60123
    • (2000) J. Europ. Math. Soc. , vol.2 , pp. 291-328
    • Lawler, G.F.1    Werner, W.2
  • 35
    • 36149042462 scopus 로고
    • Magnetic exponents of the two-dimensional q-states Potts model in two dimensions
    • B. Nienhuis, E.K. Riedel, M. Schick (1980), Magnetic exponents of the two-dimensional q-states Potts model in two dimensions, J. Phys A 13, L. 189-192.
    • (1980) J. Phys A , vol.13
    • Nienhuis, B.1    Riedel, E.K.2    Schick, M.3
  • 36
    • 29444434031 scopus 로고
    • Critical behavior in two dimensions and charge symmetry of the Coulomb gas
    • B. Nienhuis (1984), Critical behavior in two dimensions and charge symmetry of the Coulomb gas, J. Stat. Phys. 34, 731-761.
    • (1984) J. Stat. Phys. , vol.34 , pp. 731-761
    • Nienhuis, B.1
  • 37
    • 7244225886 scopus 로고
    • A relation between the temperature exponents of the eight-vertex and the q-state Potts model
    • M.P.M. den Nijs (1979), A relation between the temperature exponents of the eight-vertex and the q-state Potts model, J. Phys. A 12, 1857-1868.
    • (1979) J. Phys. A , vol.12 , pp. 1857-1868
    • Den Nijs, M.P.M.1
  • 38
    • 0001454016 scopus 로고
    • Conjecture for the extended Potts model magnetic eigenvalue
    • R.P. Pearson (1980), Conjecture for the extended Potts model magnetic eigenvalue, Phys. Rev. B 22, 2579-2580.
    • (1980) Phys. Rev. B , vol.22 , pp. 2579-2580
    • Pearson, R.P.1
  • 39
    • 0003880196 scopus 로고
    • Vandenhoeck & Ruprecht, Göttingen. MR 58:22526
    • C. Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. MR 58:22526
    • (1975) Univalent Functions
    • Pommerenke, C.1
  • 43
    • 0001193785 scopus 로고
    • Exact determination of the percolation hull exponent in two dimensions
    • MR 88d:82073
    • H. Saleur, B. Duplantier (1987), Exact determination of the percolation hull exponent in two dimensions, Phys. Rev. Lett. 58, 2325. MR 88d:82073
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 2325
    • Saleur, H.1    Duplantier, B.2
  • 44
    • 0000614574 scopus 로고    scopus 로고
    • Scaling limits of loop-erased random walks and uniform spanning trees
    • MR 2001m:60227
    • O. Schramm (2000), Scaling limits of loop-erased random walks and uniform spanning trees, Israel J. Math. 118, 221-288. MR 2001m:60227
    • (2000) Israel J. Math. , vol.118 , pp. 221-288
    • Schramm, O.1
  • 45
    • 0010699019 scopus 로고    scopus 로고
    • A percolation formula
    • MR 2002h:60227
    • O. Schramm (2001), A percolation formula, Electronic Comm. Probab. 6, 115-120. MR 2002h:60227
    • (2001) Electronic Comm. Probab. , vol.6 , pp. 115-120
    • Schramm, O.1
  • 46
    • 0041869040 scopus 로고    scopus 로고
    • Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits
    • MR 2002f:60193
    • S. Smirnov (2001), Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits, C. R. Acad. Sci. Paris Sér. I Math. 333 no. 3, 239-244. MR 2002f:60193
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , Issue.3 , pp. 239-244
    • Smirnov, S.1
  • 47
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • S. Smirnov, W. Werner (2001), Critical exponents for two-dimensional percolation, Math. Res. Lett. 8, 729-744.
    • (2001) Math. Res. Lett. , vol.8 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 48
    • 84990581872 scopus 로고
    • Brownian motion in a wedge with oblique reflection
    • MR 87c:60066
    • S.R.S. Varadhan, R.J. Williams (1985), Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. 38, 405-443. MR 87c:60066
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 405-443
    • Varadhan, S.R.S.1    Williams, R.J.2
  • 50
    • 0141430358 scopus 로고    scopus 로고
    • Critical exponents, conformal invariance and planar Brownian motion
    • Proceedings of the 4th ECM Barcelona 2000, Birkhäuser. MR 2003f:60181
    • W. Werner (2001), Critical exponents, conformal invariance and planar Brownian motion, in Proceedings of the 4th ECM Barcelona 2000, Prog. Math. 202, Birkhäuser, 87-103. MR 2003f:60181
    • (2001) Prog. Math. , vol.202 , pp. 87-103
    • Werner, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.