[Dualité des évolutions de Schramm-Loewner]
On démontre dans cette note une version de la dualité conjecturée pour les évolutions de Schramm-Loewner, en établissant des identités en distribution exactes entre certains arcs de
In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal
Keywords: Schramm-Loewner evolution, duality, partition function
Mot clés : Évolution de Schramm-Loewner, dualité, fonction de partition
@article{ASENS_2009_4_42_5_697_0, author = {Dub\'edat, Julien}, title = {Duality of {Schramm-Loewner} evolutions}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {697--724}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 42}, number = {5}, year = {2009}, doi = {10.24033/asens.2107}, zbl = {1205.60147}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.2107/} }
TY - JOUR AU - Dubédat, Julien TI - Duality of Schramm-Loewner evolutions JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 697 EP - 724 VL - 42 IS - 5 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/asens.2107/ DO - 10.24033/asens.2107 LA - en ID - ASENS_2009_4_42_5_697_0 ER -
%0 Journal Article %A Dubédat, Julien %T Duality of Schramm-Loewner evolutions %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 697-724 %V 42 %N 5 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/asens.2107/ %R 10.24033/asens.2107 %G en %F ASENS_2009_4_42_5_697_0
Dubédat, Julien. Duality of Schramm-Loewner evolutions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 5, pp. 697-724. doi : 10.24033/asens.2107. https://www.numdam.org/articles/10.24033/asens.2107/
[1]
[2] Euler integrals for commuting SLEs, Journal Statist. Phys. 123 (2006), 1183-1218. | MR | Zbl
,[3] Commutation relations for SLE, Comm. Pure Applied Math. 60 (2007), 1792-1847. | MR | Zbl
,[4] SLE and the free field: Partition functions and couplings, J. Amer. Math. Soc. 22 (2009), 995-1054. | MR | Zbl
,[5] The configurational measure on mutually avoiding SLE paths, in Universality and renormalization, Fields Inst. Commun. 50, Amer. Math. Soc., 2007, 199-224. | MR | Zbl
& ,[6] Conformal restriction: the chordal case, J. Amer. Math. Soc. 16 (2003), 917-955. | MR | Zbl
, & ,[7] Conformally invariant processes in the plane, Mathematical Surveys and Monographs 114, Amer. Math. Soc., 2005. | MR | Zbl
,[8] Conformal invariance of planar loop-erased random walks and uniform spanning trees, Ann. Probab. 32 (2004), 939-995. | MR | Zbl
, & ,[9] The Brownian loop soup, Probab. Theory Related Fields 128 (2004), 565-588. | MR | Zbl
& ,[10] Boundary behaviour of conformal maps, Grund. Math. Wiss. 299, Springer, 1992. | MR | Zbl
,[11] Continuous martingales and Brownian motion, third éd., Grund. Math. Wiss. 293, Springer, 1999. | MR | Zbl
& ,[12] Basic properties of SLE, Ann. of Math. 161 (2005), 883-924. | MR | Zbl
& ,[13] Contour lines of the two-dimensional discrete Gaussian free field, Acta Math. 202 (2009), 21-137. | MR | Zbl
& ,[14] SLE coordinate changes, New York J. Math. 11 (2005), 659-669. | EuDML | MR | Zbl
& ,
[15] Girsanov’s transformation for
[16] Random planar curves and Schramm-Loewner evolutions, in Lectures on probability theory and statistics, Lecture Notes in Math. 1840, Springer, 2004, 107-195. | MR | Zbl
,[17] Duality of chordal SLE, Invent. Math. 174 (2008), 309-353. | MR | Zbl
,[18] Reversibility of chordal SLE, Ann. Probab. 36 (2008), 1472-1494. | MR | Zbl
,- Complex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE, Annales Henri Poincaré, Volume 25 (2024) no. 1, p. 425 | DOI:10.1007/s00023-023-01300-6
- Integrability of SLE via conformal welding of random surfaces, Communications on Pure and Applied Mathematics, Volume 77 (2024) no. 5, p. 2651 | DOI:10.1002/cpa.22180
- SLE Partition Functions via Conformal Welding of Random Surfaces, International Mathematics Research Notices, Volume 2024 (2024) no. 24, p. 14763 | DOI:10.1093/imrn/rnae260
- Reversibility of whole-plane SLE for
, Probability Theory and Related Fields (2024) | DOI:10.1007/s00440-024-01333-w - The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles, Proceedings of the London Mathematical Society, Volume 128 (2024) no. 2 | DOI:10.1112/plms.12582
- Time-reversal of multiple-force-point chordal SLEκ(ρ_), Electronic Journal of Probability, Volume 28 (2023) no. none | DOI:10.1214/23-ejp1040
- Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity, Memoirs of the American Mathematical Society, Volume 289 (2023) no. 1440 | DOI:10.1090/memo/1440
- Exponents for Hamiltonian paths on random bicubic maps and KPZ, Nuclear Physics B, Volume 987 (2023), p. 116084 | DOI:10.1016/j.nuclphysb.2023.116084
- Hamiltonian cycles on bicolored random planar maps, Nuclear Physics B, Volume 995 (2023), p. 116335 | DOI:10.1016/j.nuclphysb.2023.116335
- Loewner evolution driven by complex Brownian motion, The Annals of Probability, Volume 51 (2023) no. 6 | DOI:10.1214/23-aop1639
- The topology of SLEκ is random for κ>4, Electronic Journal of Probability, Volume 27 (2022) no. none | DOI:10.1214/22-ejp871
- Large deviations of Schramm-Loewner evolutions: A survey, Probability Surveys, Volume 19 (2022) no. none | DOI:10.1214/22-ps9
- Liouville quantum gravity surfaces with boundary as matings of trees, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 57 (2021) no. 1 | DOI:10.1214/20-aihp1068
- Conformal Invariance of CLEΚ on the Riemann Sphere for Κ ∈(4,8), International Mathematics Research Notices, Volume 2021 (2021) no. 23, p. 17971 | DOI:10.1093/imrn/rnz328
- Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions, Journal of Physics A: Mathematical and Theoretical, Volume 54 (2021) no. 32, p. 325002 | DOI:10.1088/1751-8121/ac0dee
- Generalized disconnection exponents, Probability Theory and Related Fields, Volume 179 (2021) no. 1-2, p. 117 | DOI:10.1007/s00440-020-01005-5
- On the uniqueness of global multiple SLEs, The Annals of Probability, Volume 49 (2021) no. 1 | DOI:10.1214/20-aop1477
- External diffusion-limited aggregation on a spanning-tree-weighted random planar map, The Annals of Probability, Volume 49 (2021) no. 4 | DOI:10.1214/20-aop1486
- Hypergeometric SLE: Conformal Markov Characterization and Applications, Communications in Mathematical Physics, Volume 374 (2020) no. 2, p. 433 | DOI:10.1007/s00220-020-03697-1
- Large deviations of radial SLE
, Electronic Journal of Probability, Volume 25 (2020) no. none | DOI:10.1214/20-ejp502 - Dimension transformation formula for conformal maps into the complement of an SLE curve, Probability Theory and Related Fields, Volume 176 (2020) no. 1-2, p. 649 | DOI:10.1007/s00440-019-00952-y
- First passage sets of the 2D continuum Gaussian free field, Probability Theory and Related Fields, Volume 176 (2020) no. 3-4, p. 1303 | DOI:10.1007/s00440-019-00941-1
- A multifractal boundary spectrum for
, Probability Theory and Related Fields, Volume 178 (2020) no. 1-2, p. 173 | DOI:10.1007/s00440-020-00975-w - An almost sure KPZ relation for SLE and Brownian motion, The Annals of Probability, Volume 48 (2020) no. 2 | DOI:10.1214/19-aop1385
- Connectivity properties of the adjacency graph of
bubbles for , The Annals of Probability, Volume 48 (2020) no. 3 | DOI:10.1214/19-aop1402 - Harmonic functions on mated-CRT maps, Electronic Journal of Probability, Volume 24 (2019) no. none | DOI:10.1214/19-ejp325
- Bipolar orientations on planar maps and
, The Annals of Probability, Volume 47 (2019) no. 3 | DOI:10.1214/18-aop1282 - Gaussian free field light cones and
, The Annals of Probability, Volume 47 (2019) no. 6 | DOI:10.1214/18-aop1331 - Dimension of the SLE Light Cone, the SLE Fan, and
SLE κ ( ρ ) for κ ∈ ( 0 , 4 ) and ρ ∈ [ κ 2 - 4 , - 2 ), Communications in Mathematical Physics, Volume 360 (2018) no. 3, p. 1083 | DOI:10.1007/s00220-018-3109-9 - Connection Probabilities for Conformal Loop Ensembles, Communications in Mathematical Physics, Volume 362 (2018) no. 2, p. 415 | DOI:10.1007/s00220-018-3207-8
- Almost sure multifractal spectrum of Schramm–Loewner evolution, Duke Mathematical Journal, Volume 167 (2018) no. 6 | DOI:10.1215/00127094-2017-0049
- Chordal SLE
explorations of a quantum disk, Electronic Journal of Probability, Volume 23 (2018) no. none | DOI:10.1214/18-ejp161 - Polychromatic Arm Exponents for the Critical Planar FK-Ising Model, Journal of Statistical Physics, Volume 170 (2018) no. 6, p. 1177 | DOI:10.1007/s10955-018-1983-3
- Alternating arm exponents for the critical planar Ising model, The Annals of Probability, Volume 46 (2018) no. 5 | DOI:10.1214/17-aop1241
- Boundary arm exponents for SLE, Electronic Journal of Probability, Volume 22 (2017) no. none | DOI:10.1214/17-ejp110
- CLE PERCOLATIONS, Forum of Mathematics, Pi, Volume 5 (2017) | DOI:10.1017/fmp.2017.5
- Intersections of SLE Paths: the double and cut point dimension of SLE, Probability Theory and Related Fields, Volume 167 (2017) no. 1-2, p. 45 | DOI:10.1007/s00440-015-0677-x
- Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees, Probability Theory and Related Fields, Volume 169 (2017) no. 3-4, p. 729 | DOI:10.1007/s00440-017-0780-2
- Level lines of Gaussian Free Field I: Zero-boundary GFF, Stochastic Processes and their Applications, Volume 127 (2017) no. 4, p. 1045 | DOI:10.1016/j.spa.2016.07.009
- An
loop measure, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 52 (2016) no. 3 | DOI:10.1214/15-aihp681 - Imaginary geometry III: reversibility of _κfor κ∈(4,8), Annals of Mathematics, Volume 184 (2016) no. 2, p. 455 | DOI:10.4007/annals.2016.184.2.3
- Active spanning trees and Schramm-Loewner evolution, Physical Review E, Volume 93 (2016) no. 6 | DOI:10.1103/physreve.93.062121
- Imaginary geometry I: interacting SLEs, Probability Theory and Related Fields, Volume 164 (2016) no. 3-4, p. 553 | DOI:10.1007/s00440-016-0698-0
- Imaginary geometry II: Reversibility of
for , The Annals of Probability, Volume 44 (2016) no. 3 | DOI:10.1214/14-aop943 - SLE and Virasoro Representations: Localization, Communications in Mathematical Physics, Volume 336 (2015) no. 2, p. 695 | DOI:10.1007/s00220-014-2282-8
- SLE and Virasoro Representations: Fusion, Communications in Mathematical Physics, Volume 336 (2015) no. 2, p. 761 | DOI:10.1007/s00220-014-2283-7
- From CLE(
) to SLE( )'s, Electronic Journal of Probability, Volume 18 (2013) no. none | DOI:10.1214/ejp.v18-2376 - Conformally invariant scaling limits in planar critical percolation, Probability Surveys, Volume 8 (2011) no. none | DOI:10.1214/11-ps180
- Oded Schramm: From Circle Packing to SLE, Selected Works of Oded Schramm (2011), p. 3 | DOI:10.1007/978-1-4419-9675-6_1
- Oded Schramm: From circle packing to SLE, The Annals of Probability, Volume 39 (2011) no. 5 | DOI:10.1214/10-aop590
- Duality of chordal SLE, II, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 46 (2010) no. 3 | DOI:10.1214/09-aihp340
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