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In this note, we establish an expression of the Loewner energy of a Jordan curve on the Riemann sphere in terms of Werner's measure on simple loops of SLE$_{8/3}$ type.
Untersuchungen über schlichte konforme abbildungen des einheitskreises. i
Loewner, K.: · 1923
Earlier work this paper cites.
On Löwner differential equation
Pommerenke, C.: · 1966
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R R -Torsion and the Laplacian on Riemannian manifolds
Ray, D.B., Singer, I.M.: · 1971
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A proof of the Bieberbach conjecture
De Branges, L.,: · 1985
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Scaling limits of loop-erased random walks and uniform spanning trees
Schramm, O.: · 2000
Earlier work this paper cites.
Conformal restriction: the chordal case
Lawler, G., Schramm, O., Werner, W.: · 2003
Earlier work this paper cites.
The Brownian loop soup
Lawler, G., Werner, W.: · 2004
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Markov loops, determinants and Gaussian fields
Le Jan, Y., · 2006
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Weil-Petersson metric on the universal Teichmuller space
Takhtajan, L.A., Teo, L.-P.: · 2006
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Commutation relations for Schramm-Loewner evolutions
Dubédat, J.: · 2007
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The conformally invariant measure on self-avoiding loops
Werner, W.: · 2008
Cited alongside, same era.
SLE and the free field: partition functions and couplings
Dubédat, J.: · 2009
Cited alongside, same era.
Random soups, carpets and fractal dimensions
Nacu, S., Werner, W.: · 2011
Later among the works it cites.
The nested simple conformal loop ensembles in the Riemann sphere
Kemppainen, A., Werner, W.: · 2016
Later among the works it cites.
The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE 0 + \mbox{SLE}_{0+}
Wang, Y.: · 2016
Later among the works it cites.
On the existence of SLE trace: finite energy drivers and non constant κ \kappa
Friz, P., Shekhar, A.: · 2017
Later among the works it cites.
The Loewner energy of loops and regularity of driving functions
Rohde, S., Wang, Y.: · 2017
Later among the works it cites.
Geometric descriptions of the Loewner energy
Wang, Y.: · 2018
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