SLE as a Mating of Trees in Euclidean Geometry

[1]  Dapeng Zhan,et al.  Multipoint Estimates for Radial and Whole-Plane SLE , 2017, Journal of Statistical Physics.

[2]  S. Benoist.  Natural parametrization of SLE: the Gaussian free field point of view , 2017, 1708.03801.

[3]  Samuel S. Watson,et al.  Schnyder woods, SLE$_{(16)}$, and Liouville quantum gravity , 2017, 1705.03573.

[4]  G. Lawler,et al.  Convergence of radial loop-erased random walk in the natural parametrization , 2017, 1703.03729.

[5]  S. Smirnov,et al.  Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE , 2016, 1609.08527.

[6]  S. Sheffield,et al.  Imaginary geometry III: reversibility of SLE_κ for κ\in (4,8) , 2016 .

[7]  N. Holden,et al.  A distance exponent for Liouville quantum gravity , 2016, 1606.01214.

[8]  D. Wilson,et al.  Six-vertex model and Schramm-Loewner evolution. , 2016, Physical review. E.

[9]  S. Sheffield,et al.  Imaginary geometry II: Reversibility of SLE[subscript κ](ρ[subscript 1];ρ[subscript 2]) for κ ∈ (0,4) , 2016 .

[10]  N. Holden,et al.  Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense , 2016, 1603.01194.

[11]  Jason Miller,et al.  An almost sure KPZ relation for SLE and Brownian motion , 2015, The Annals of Probability.

[12]  D. Wilson,et al.  Bipolar orientations on planar maps and SLE$_{12}$ , 2015, 1511.04068.

[13]  Xin Sun,et al.  Scaling limits for the critical Fortuin-Kastelyn model on a random planar map III: finite volume case , 2015, 1510.06346.

[14]  Nathanael Berestycki,et al.  An elementary approach to Gaussian multiplicative chaos , 2015, 1506.09113.

[15]  Xin Sun,et al.  Scaling limits for the critical Fortuin-Kastelyn model on a random planar map II: local estimates and empty reduced word exponent , 2015, 1505.03375.

[16]  Cheng Mao,et al.  Scaling limits for the critical Fortuin–Kasteleyn model on a random planar map I: Cone times , 2015, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[17]  V. Vargas,et al.  Liouville Quantum Gravity on the Riemann Sphere , 2014, Communications in Mathematical Physics.

[18]  S. Sheffield,et al.  Liouville quantum gravity as a mating of trees , 2014, 1409.7055.

[19]  M. Barlow,et al.  Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree , 2014, 1407.5162.

[20]  H. Duminil-Copin,et al.  Convergence of Ising interfaces to Schramm's SLE curves , 2013, 1312.0533.

[21]  Vincent Vargas,et al.  Gaussian multiplicative chaos and applications: A review , 2013, 1305.6221.

[22]  S. Sheffield,et al.  Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees , 2013, 1302.4738.

[23]  G. Lawler,et al.  Minkowski content and natural parameterization for the Schramm–Loewner evolution , 2012, 1211.4146.

[24]  R. Abraham,et al.  A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces , 2012, 1202.5464.

[25]  S. Sheffield,et al.  Imaginary geometry I: interacting SLEs , 2012, 1201.1496.

[26]  S. Sheffield.  Quantum gravity and inventory accumulation , 2011, 1108.2241.

[27]  S. Sheffield.  Conformal weldings of random surfaces: SLE and the quantum gravity zipper , 2010, 1012.4797.

[28]  M. Barlow,et al.  Exponential tail bounds for loop-erased random walk in two dimensions , 2009, 0910.5015.

[29]  S. Smirnov,et al.  Universality in the 2D Ising model and conformal invariance of fermionic observables , 2009, 0910.2045.

[30]  Robert Masson.  The growth exponent for planar loop-erased random walk , 2008, 0806.0357.

[31]  Julien Dubédat.  SLE and the free field: partition functions and couplings , 2007, 0712.3018.

[32]  O. Schramm,et al.  Contour lines of the two-dimensional discrete Gaussian free field , 2006, math/0605337.

[33]  Olivier Bernardi,et al.  Bijective Counting of Tree-Rooted Maps and Shuffles of Parenthesis Systems , 2006, Electron. J. Comb..

[34]  J. L. Gall,et al.  Random trees and applications , 2005, math/0511515.

[35]  S. Sheffield.  Gaussian free fields for mathematicians , 2003, math/0312099.

[36]  O. Schramm,et al.  Conformal invariance of planar loop-erased random walks and uniform spanning trees , 2001, math/0112234.

[37]  S. Smirnov.  Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits , 2001 .

[38]  Oded Schramm,et al.  Scaling limits of loop-erased random walks and uniform spanning trees , 1999, math/9904022.

[39]  David Bruce Wilson,et al.  Generating random spanning trees more quickly than the cover time , 1996, STOC '96.

[40]  Jason Miller,et al.  Brownian motion correlation in the peanosphere for κ > 8 , 2016 .

[41]  S. Sheffield,et al.  Imaginary geometry II: Reversibility of SLEκ(ρ1;ρ2) for κ∈(0,4). , 2016 .

[42]  Gregory,et al.  A NATURAL PARAMETRIZATION FOR THE SCHRAMM–LOEWNER EVOLUTION , 2011 .

[43]  Gregory F. Lawler,et al.  Conformally Invariant Processes in the Plane , 2005 .

[44]  D. Aldous.  Stochastic Analysis: The Continuum random tree II: an overview , 1991 .

[45]  David Aldous,et al.  The Continuum Random Tree III , 1991 .

[46]  R. Mullin,et al.  On the Enumeration of Tree-Rooted Maps , 1967, Canadian Journal of Mathematics.

[47]  Yu. V. Prokhorov.  Convergence of Random Processes and Limit Theorems in Probability Theory , 1956 .