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G\'{e}rard Watts predicted a formula for the probability in percolation that there is both a left--right and an up--down crossing, which was later proved by Julien Dub\'{e}dat.
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Schramm, OdedO. andSheffield, ScottS. (2005). Harmonic explorer and its convergence to SLE 4 {\rm SLE}_{4} . Ann. Probab. 33 2127–2148
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Camia, FedericoF. andNewman, Charles M.C. M. (2007). Critical percolation exploration path and SLE 6 {\rm SLE}_{6} : A proof of convergence. Probab. Theory Related Fields 139 473–519
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Simmons, Jacob J. H.J. J. H., Kleban, PeterP. andZiff, Robert M.R. M. (2007). Percolation crossing formulae and conformal field theory. J. Phys. A 40 F771–F784
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Dubédat, JulienJ. (2006a). Excursion decompositions for SLE and Watts’ crossing formula. Probab. Theory Related Fields 134 453–488
Cited in the paper.
Dubédat, JulienJ. (2006b). Euler integrals for commuting SLEs. J. Stat. Phys. 123 1183–1218
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2009
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