@phdthesis{BJHTUP11_2003__0634__A1_0, author = {Beffara, Vincent}, title = {Mouvement brownien plan, {SLE,} invariance conforme et dimensions fractales}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e Paris XI UFR scientifique d'Orsay}, number = {634}, year = {2003}, language = {fr}, url = {http://www.numdam.org/item/BJHTUP11_2003__0634__A1_0/} }
TY - BOOK AU - Beffara, Vincent TI - Mouvement brownien plan, SLE, invariance conforme et dimensions fractales T3 - Thèses d'Orsay PY - 2003 IS - 634 PB - Université Paris XI UFR scientifique d'Orsay UR - http://www.numdam.org/item/BJHTUP11_2003__0634__A1_0/ LA - fr ID - BJHTUP11_2003__0634__A1_0 ER -
Beffara, Vincent. Mouvement brownien plan, SLE, invariance conforme et dimensions fractales. Thèses d'Orsay, no. 634 (2003), 138 p. http://numdam.org/item/BJHTUP11_2003__0634__A1_0/
[1] Conformal Invariants, Topics in Geometric Function Theory, McGraw- Hill, New York, 1973. | MR | Zbl
,[2] Diffusions and elliptic operators. Probability and Its Applications, Springer, 1998. | MR | Zbl
,[3] Cutting Brownian Paths, vol. 657 of Memoirs of the American Mathematical Society, AMS, 1999. | Zbl | MR
and ,[4] The supremum of Brownian local times on Holder curves, Annales de l'institut Henri Poincarré, 37 (2001), pp. 627-642. | MR | Zbl | Numdam | DOI
and ,[5] On conformally invariant subsets of the planar Brownian curve, Preprint, arXiv :math.PR/0105192, (2001). | MR | Zbl | Numdam
,[6] when , In preparation, (2002).
,[7] Cut points on Brownian paths, Ann. Probab., 17 (1989), pp. 1012-1036. | MR | Zbl | DOI
,[8] On the support of harmonic measure for sets of Cantor type, Ann. Acad. Sci. Fenn. Ser. A I Math, 10 (1985), pp. 113-123. | MR | Zbl | DOI
,[9] On coefficient problems for univalent functions and conformal dimension, Duke Mathematical Journal, 66 (1992), pp. 169-206. | MR | Zbl | DOI
and ,[10] Julia and John, Bol. Soc. Bras. Mat., 25 (1994), pp. 1-30. | MR | Zbl | DOI
, , and ,[11] An extension of a result of Burdzy and Lawler, Probab. Theory Relat. Fields, 89 (1991), pp. 487-502. | MR | Zbl | DOI
and ,[12] Large Deviations Techniques and Applications, Springer, 2 ed., 1998. | MR | Zbl
and ,[13] Éléments de Physique Statistique, Hermann, 1989.
, , , and ,[14] Conformally invariant fractals and potential theory, Phys. Rev. Lett., 84 (2000), pp. 1363-1367. | MR | Zbl | DOI
,[15] Univalent Functions, Springer-Verlag, 1983. | MR | Zbl
,[16] On the Hausdorff dimension of Brownian cone points, Math. Proc. Camb. Phil. Soc., 98 (1985), pp. 343-353. | MR | Zbl | DOI
,[17] Conformal fields, restriction properties, degenerate representations and SLE, Preprint, arXiv :math. PR/0209382, (2002). | MR | Zbl | DOI
and ,[18] Lectures on conformal field theory. | Zbl
,[19] Percolation, Springer-Verlag, 1989. | MR | Zbl | DOI
,[20] Density properties of harmonic measure. Annals of Mathematics, 142 (1995), pp. 427-455. | MR | Zbl
and ,[21] Some Random Series of Functions, vol. 5 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2 ed., 1993. | Zbl
,[22] Une propriété métrique du mouvement brownien, C.R. Acad. Sci., A 268 (1969), pp. 727-728. | MR | Zbl
,[23] Conformal invariance in two-dimensional percolation, Bulletin of the A.M.S., 30 (1994). | MR | Zbl | DOI
, , and ,[24] The dimension of the frontier of planar Brownian motion, Elect. Comm, in Probab., 1 (1996), pp. 29-47. | MR | Zbl
,[25] Hausdorff dimension of cut points for Brownian motion. Electronic Journal of Probability, 1 (1996), pp. 1-20. | MR | Zbl
,[26] Strict concavity of the intersection exponent for Brownian motion in two and three dimensions, Mathematical Physics Electronic Journal, 4 (1998). | MR | Zbl
,[27] Geometric and fractal properties of Brownian motion and random walk paths in two and three dimensions, in Random Walks (Budapest, 1998), vol. 9 of Bolyai Soc. Math. Stud., 1999, pp. 219-258. | MR | Zbl
,[28] The intersection exponent for simple random walks, Comb. Prob. Comp., 9 (2000), pp. 441-464. | MR | Zbl | DOI
and ,[29] Conformal restriction : The chordal case, Preprint, arXiv :math.PR/0209343, (2001). | MR | Zbl
, , and ,[30] The dimension of the Brownian frontier is 4/3, Math. Rev. Lett., 8 (2001), pp. 13-24. | MR | Zbl | DOI
, , and ,[31] Values of Brownian intersection exponents I : Half-plane exponents, Acta Mathematica, 187 (2001), pp. 237-273. | MR | Zbl | DOI
, , and ,[32] Values of Brownian intersection exponents II : Plane exponents, Acta Mathematica, 187 (2001), pp. 275-308. | MR | Zbl | DOI
, , and ,[33] Analyticity of intersection exponents for planar Brownian motion, To appear in Acta Mathematica, 188 (2002). | MR | Zbl
, , and ,[34] Conformal invariance of planar loop-erased random walks and uniform spanning trees, Preprint, arXiv :math.PR/0112234, (2002). | MR | Zbl
, , and ,[35] On the scaling limit of planar self-avoiding walks, Preprint, arXiv :math.PR/0204277, (2002). | MR | Zbl
, , and ,[36] Values of Brownian intersection exponents III : Two-sided exponents, Annales Inst. Henri Poincaré PR, 38 (2002), pp. 109-123. | MR | Zbl | Numdam | DOI
, , and ,[37] Intersection exponents for planar Brownian motion, Ann. Probab., (1999), pp. 1601-1642. | MR | Zbl
and ,[38] Some properties of planar Brownian motion, in École d'été de Probabilités de Saint-Flour XX-1990, vol. 1527 of Lecture Notes in Mathematics, Springer, 1992. | MR | Zbl
,[39] The pivot algorithm : A highly efficient Monte-Carlo method for the self-avoiding walk, Journal of Statistical Physics, 50 (1988), pp. 109-186. | MR | Zbl | DOI
and ,[40] Geometry of sets and measures in Euclidean spaces, vol. 44 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, 1995. | MR | Zbl
,[41] Boundary Behaviour of Conformal Maps, Springer, 1992. | MR | Zbl | DOI
,[42] Basic properties of SLE, Preprint, arXiv :math.PR/0106036, (2001). | Zbl
and ,[43] Scaling limits of loop-erased random walks and uniform spanning trees, Israel Journal of Mathematics, 118 (2000), pp. 221-288. | MR | Zbl | DOI
,[44] Critical percolation in the plane : Conformal invariance, Cardy's formula, scaling limits, C. R. Acad. Sci. Paris Ser. I Math., 333 (2001), pp. 239-244. | MR | Zbl
,[45] Critical exponents for two-dimensional percolation, Mathematical Research Letters, 8 (2001), pp. 729-744. | MR | Zbl | DOI
and ,[46] On Brownian disconnection exponents, Bernoulli, 1 (1995), pp. 371-380. | MR | Zbl | DOI
,[47] Bounds for disconnection exponents, Elect. Comm, in Probab., 1 (1996), pp. 19-28. | MR | Zbl
,[48] Critical exponents, conformal invariance and planar Brownian motion, in Proceedings of the 3rd European Mathematical Congress, Birkhäuser, 2000. | MR | Zbl
,[49] On univalent functions in multiply connected domains, Journal of the Beijing Institute of Technology, 3 (1994), pp. 99-113. | MR | Zbl
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