메뉴 건너뛰기




Volumn 140, Issue 6, 2010, Pages 1115-1129

Exact Sampling of Self-avoiding Paths via Discrete Schramm-Loewner Evolution

Author keywords

Exact sampling; Natural parametrization; Schramm Loewner evolution; Self avoiding walk

Indexed keywords


EID: 77956180191     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-010-0031-8     Document Type: Article
Times cited : (6)

References (26)
  • 4
    • 0042870222 scopus 로고    scopus 로고
    • Square lattice self-avoiding walks and polygons
    • Guttmann, A. J., Conway, A. R.: Square lattice self-avoiding walks and polygons. Ann. Comb. 5, 319-345 (2001).
    • (2001) Ann. Comb. , vol.5 , pp. 319-345
    • Guttmann, A.J.1    Conway, A.R.2
  • 5
    • 16144367349 scopus 로고    scopus 로고
    • Monte Carlo methods for the self-avoiding walk
    • Sokal, A. D.: Monte Carlo methods for the self-avoiding walk. Nucl. Phys. B 47, 172-179 (1996).
    • (1996) Nucl. Phys. B , vol.47 , pp. 172-179
    • Sokal, A.D.1
  • 6
    • 70449559077 scopus 로고    scopus 로고
    • Monte Carlo methods for the self-avoiding walk
    • 323001
    • Janse van Rensburg, E. J.: Monte Carlo methods for the self-avoiding walk. J. Phys. A, Math. Theor. 42, 323001 (2009).
    • (2009) J. Phys. A, Math. Theor. , vol.42
    • Janse van Rensburg, E.J.1
  • 7
    • 33646495504 scopus 로고    scopus 로고
    • On the scaling limit of planar self-avoiding walks
    • Lawler, G. F., Schramm, O., Werner, W.: On the scaling limit of planar self-avoiding walks. Proc. Symp. Pure Math. 72(2), 339-364 (2004).
    • (2004) Proc. Symp. Pure Math. , vol.72 , Issue.2 , pp. 339-364
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 8
    • 34548570078 scopus 로고    scopus 로고
    • The length of an SLE-Monte Carlo studies
    • Kennedy, T.: The length of an SLE-Monte Carlo studies. J. Stat. Phys. 128, 1263-1277 (2007).
    • (2007) J. Stat. Phys. , vol.128 , pp. 1263-1277
    • Kennedy, T.1
  • 9
    • 70350364759 scopus 로고    scopus 로고
    • Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: A numerical study
    • Gherardi, M.: Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: a numerical study. J. Stat. Phys. 136, 864-874 (2009).
    • (2009) J. Stat. Phys. , vol.136 , pp. 864-874
    • Gherardi, M.1
  • 10
    • 85204080612 scopus 로고    scopus 로고
    • Lawler, G. F.: Dimension and natural parametrization for SLE curves. Preprint. arXiv: 0712. 3263v1 [math. PR].
  • 11
    • 85204062211 scopus 로고    scopus 로고
    • Lawler, G. F., Sheffield, S.: The natural parametrization for the Schramm-Loewner evolution. Preprint. arXiv: 0906. 3804v1 [math. PR].
  • 12
    • 20044391014 scopus 로고    scopus 로고
    • Mathematical Surveys and Monographs, Providence: American Mathematical Society
    • Lawler, G. F.: Conformally invariant processes in the plane. In: Mathematical Surveys and Monographs, vol. 114. American Mathematical Society, Providence (2005).
    • (2005) Conformally Invariant Processes in the Plane , vol.114
    • Lawler, G.F.1
  • 13
    • 14944350573 scopus 로고    scopus 로고
    • Random planar curves and Schramm-Loewner evolutions (Lecture notes from the 2002 Saint-Flour summer school)
    • Werner, W.: Random planar curves and Schramm-Loewner evolutions (Lecture notes from the 2002 Saint-Flour summer school). L. N. Math. 1840, 107-195 (2004).
    • (2004) L. N. Math. , vol.1840 , pp. 107-195
    • Werner, W.1
  • 14
    • 20444484481 scopus 로고    scopus 로고
    • SLE for theoretical physicists
    • Cardy, J.: SLE for theoretical physicists. Ann. Phys. 318, 81-118 (2005).
    • (2005) Ann. Phys. , vol.318 , pp. 81-118
    • Cardy, J.1
  • 15
    • 3543011408 scopus 로고    scopus 로고
    • A guide to stochastic Loewner evolution and its applications
    • Kager, W., Nienhuis, B.: A guide to stochastic Loewner evolution and its applications. J. Stat. Phys. 115, 1149-1229 (2004).
    • (2004) J. Stat. Phys. , vol.115 , pp. 1149-1229
    • Kager, W.1    Nienhuis, B.2
  • 16
    • 33748574926 scopus 로고    scopus 로고
    • 2D growth processes: SLE and Loewner chains
    • Bauer, M., Bernard, D.: 2D growth processes: SLE and Loewner chains. Phys. Rept. 432, 115-221 (2006).
    • (2006) Phys. Rept. , vol.432 , pp. 115-221
    • Bauer, M.1    Bernard, D.2
  • 17
    • 10644272080 scopus 로고    scopus 로고
    • Discrete Löwner evolution
    • Bauer, R. O.: Discrete Löwner evolution. Ann. Fac. Sci. Toulouse VI 12, 433-451 (2003).
    • (2003) Ann. Fac. Sci. Toulouse VI , vol.12 , pp. 433-451
    • Bauer, R.O.1
  • 18
    • 85204030298 scopus 로고    scopus 로고
    • Kennedy, T.: Monte Carlo comparisons of the self-avoiding walk and SLE as parametrized curves. Preprint. arXiv: math/0612609v2 [math. PR].
  • 19
    • 4243632346 scopus 로고
    • Diffusion-limited aggregation: A kinetic critical phenomenon
    • Witten, T. A., Sander, L. M.: Diffusion-limited aggregation: A kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400-1403 (1981).
    • (1981) Phys. Rev. Lett. , vol.47 , pp. 1400-1403
    • Witten, T.A.1    Sander, L.M.2
  • 20
    • 22244445187 scopus 로고    scopus 로고
    • Laplacian growth as one-dimensional turbulence
    • Hastings, M. B., Levitov, L. S.: Laplacian growth as one-dimensional turbulence. Physica D 116, 244-252 (1998).
    • (1998) Physica D , vol.116 , pp. 244-252
    • Hastings, M.B.1    Levitov, L.S.2
  • 21
    • 0000614574 scopus 로고    scopus 로고
    • Scaling limits of loop-erased random walks and uniform spanning trees
    • Schramm, O.: 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
  • 22
    • 4243471694 scopus 로고    scopus 로고
    • Exact multifractal spectra for arbitrary Laplacian random walks
    • 055506
    • Hastings, M. B.: Exact multifractal spectra for arbitrary Laplacian random walks. Phys. Rev. Lett. 88, 055506 (2002).
    • (2002) Phys. Rev. Lett. , vol.88
    • Hastings, M.B.1
  • 23
    • 5944256461 scopus 로고
    • The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk
    • Madras, N., Sokal, A. D.: The pivot algorithm: a highly efficient Monte Carlo method for the self-avoiding walk. J. Stat. Phys. 50, 109-186 (1988).
    • (1988) J. Stat. Phys. , vol.50 , pp. 109-186
    • Madras, N.1    Sokal, A.D.2
  • 24
    • 0141560572 scopus 로고    scopus 로고
    • A Faster implementation of the pivot algorithm for self-avoiding walks
    • Kennedy, T.: A Faster implementation of the pivot algorithm for self-avoiding walks. J. Stat. Phys. 106, 407-429 (2002).
    • (2002) J. Stat. Phys. , vol.106 , pp. 407-429
    • Kennedy, T.1
  • 25
    • 85204072011 scopus 로고    scopus 로고
    • Saleur, H.: Conformal invariance for polymers and percolation. J. Phys. A, Math. Gen. 20 (1987).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.