Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits

Stanislav Smirnov

Type: Article

Publication Date: 2001-08-01

Citations: 760

DOI: https://doi.org/10.1016/s0764-4442(01)01991-7

View Publication

Download PDF

Locations

Comptes Rendus de l Académie des Sciences - Series I - Mathematics - View
arXiv (Cornell University) - PDF

Similar Works

Action	Title	Year	Authors
+	Critical percolation in the plane : I. Conformal invariance and Cardy's formula. II. Continuum scaling limit	2001	Stanislav Smirnov
+	Critical percolation in the plane	2009	Stanislav Smirnov
+ PDF Chat	Is Critical 2D Percolation Universal?	2008	Vincent Beffara
+	Is critical 2D percolation universal?	2007	Vincent Beffara
+ PDF Chat	Critical percolation and conformal invariance	2006	Stanislav Smirnov
+ PDF Chat	Critical percolation: the expected number of clusters in a rectangle	2010	Clément Hongler Stanislav Smirnov
+	Conformally invariant scaling limits in planar critical percolation	2009	Nike Sun
+	A generalization of Cardy's and Schramm's formulae	2023	Mikhail Khristoforov Mikhail Skopenkov Stanislav Smirnov
+ PDF Chat	Conformally invariant scaling limits in planar critical percolation	2011	Nike Sun
+	Critical percolation: the expected number of clusters in a rectangle	2009	Clément Hongler Stanislav Smirnov
+	Percolation and $O(1)$ loop model	2021	Mikhail Khristoforov Stanislav Smirnov
+	Percolation and $O(1)$ loop model	2021	Mikhail Khristoforov Stanislav Smirnov
+	Conformal invariance – Smirnov's Theorem	2006	Béla Bollobás Oliver Riordan
+ PDF Chat	Critical site percolation on the triangular lattice: from integrability to conformal partition functions	2023	Alexi Morin-Duchesne Andreas Klümper Paul A. Pearce
+	Universal aspects of critical percolation on random half-planar maps	2014	Loïc Richier
+ PDF Chat	Universal aspects of critical percolation on random half-planar maps	2015	Loïc Richier
+	Universal aspects of critical percolation on random half-planar maps	2014	Loïc Richier
+	Conformal Covariance of Connection Probabilities and Fields in 2D Critical Percolation	2022	Federico Camia
+ PDF Chat	Conformal invariance in three dimensional percolation	2015	Giacomo Gori Andrea Trombettoni
+	Conformal invariance of the exploration path in 2-d critical bond percolation in the square lattice	2011	Jonathan Tsai Sheung Chi Phillip Yam Wang Zhou

Works That Cite This (708)

Action	Title	Year	Authors
+	Dipolar Komatu–Loewner differential equation	2024	Shiyi Lan Su-Yang Li
+ PDF Chat	Percolation of random nodal lines	2017	Vincent Beffara Damien Gayet
+ PDF Chat	Bond percolation on isoradial graphs: criticality and universality	2013	Geoffrey Grimmett Ioan Manolescu
+ PDF Chat	Computing the Loewner Driving Process of Random Curves in the Half Plane	2008	Tom Kennedy
+ PDF Chat	Convergence of uniform triangulations under the Cardy embedding	2023	Nina Holden Xin Sun
+ PDF Chat	Conformal Loop Ensembles and the Stress–Energy Tensor	2012	Benjamin Doyon
+ PDF Chat	Oded Schramm’s contributions to noise sensitivity	2011	Christophe Garban
+	Perturbation of the tangential slit by conformal maps	2018	Hai-Hua Wu Yue-Ping Jiang Xin‐Han Dong
+ PDF Chat	Percolation and coarse conformal uniformization	2018	Itaı Benjamini
+	Conformal invariance and Renormalization Group	2020	Alessandro Giuliani

Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	Critical Exponents, Conformal Invariance and Planar Brownian Motion	2001	Wendelin Werner
+ PDF Chat	Path-Crossing Exponents and the External Perimeter in 2D Percolation	1999	Michael Aizenman Bertrand Duplantier Amnon Aharony
+	Hölder regularity and dimension bounds for random curves	1999	Michael Aizenman Almut Burchard
+ PDF Chat	Conformal invariance in two-dimensional percolation	1994	R. P. Langlands Philippe Pouliot Yvan Saint-Aubin
+ PDF Chat	Values of Brownian intersection exponents, II: Plane exponents	2001	Gregory F. Lawler Oded Schramm Wendelin Werner
+ PDF Chat	The Dimension of the Planar Brownian Frontier is 4/3	2001	Gregory F. Lawler Oded Schramm Wendelin Werner
+ PDF Chat	The Dimension of the Planar Brownian Frontier is 4/3	2001	Gregory F. Lawler Oded Schramm Wendelin Werner
+ PDF Chat	Critical percolation in finite geometries	1992	John Cardy
+	Values of Brownian intersection exponents, I: Half-plane exponents	2011	Gregory F. Lawler Oded Schramm Wendelin Werner