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References
- M. Aizenmann and G. Grimmett, Strict Monotonicity for Critical Points in Percolation and Ferromagnetic Models, J. Stat. Phys. 63 (1991) 817-835 Math. Review 92i:82060
- H. Bierme and A. Estrade, Covering the whole space with Poisson random ball in preparation (2010)
- E.I. Broman and F. Camia, Large-$N$ limit of crossing probabilities, discontinuity, and asymptotic behavior of threshold values in Mandelbrot's fractal percolation process, Electron. J. Probab. 13 (2008) 980-999 Math. Review 2009g:60130
- R.M. Burton and M. Keane, Density and Uniqueness in Percolation, Comm. Math. Phys. 121 (1989) 501-505 Math. Review 90g:60090
- J.T. Chayes and L. Chayes, The large-$N$ limit of the threshold values in Mandelbrot's fractal percolation process, J.Phys.A: Math. Gen. 22 (1989) L501--L506 Math. Review 90h:82044
- J.T. Chayes, L. Chayes and R. Durrett, Connectivity Properties of Mandelbrot's Percolation Process, Probab. Theory Relat. Fields 77 (1988) 307-324 Math. Review 89d:60193
- J.T. Chayes, L. Chayes, E. Grannan and G. Swindle, Phase transitions in Mandelbrot's percolation process in three Probab. Theory Relat. Fields 90 (1991) 291-300 Math. Review 93a:60156
- L. Chayes, Aspects of the fractal percolation process, Progress in Probability 37 (1995) 113-143 Math. Review 97g:60131
- F.M. Dekking and G.R. Grimmett, Superbranching processes and projections of random Cantor sets, Probab. Theory Relat. Fields 78 (1988) 335-355 Math. Review 89f:60099
- F.M. Dekking and R.W.J. Meester, On the structure of Mandelbrot's percolation process and other Random Cantor sets J. Stat. Phys. 58 (1990) 1109-1126 Math. Review 91c:60140
- K.J. Falconer Fractal Geometry Second edition, Wiley, Chichester, 2003. Math. Review 2006b:28001
- K.J. Falconer and G.R. Grimmett, The critical point of fractal percolation in three and more dimensions, J. Phys. A: Math. Gen. 24 (1991) L491--L494 Math. Review 92g:82053
- K.J. Falconer and G.R. Grimmett, On the geometry of Random Cantor Sets and Fractal Percolation, J. Theor. Probab. 5 (1992) 465-485 Math. Review 94b:60115
- B. Freivogel and M. Kleban, A Conformal Field Theory for Eternal Inflation? J. High Energy Phys. 12 (2009) 019 Math. Review number not available
- G. Grimmett, Percolation Second edition, Springer-Verlag, Berlin 1999 Math. Review 2001a:60114
- S. Janson, Bounds of the distribution of extremal values of a scanning process, Stochastic Process. Appl. 18 (1984) 313-328. Math. Review 86f:60066
- G.F. Lawler, Conformally Invariant Processes in the Plane Mathematical Surveys and Monographs, 114. American Mathematical Society, Providence, 2005 Math. Review 2006i:60003
- G.F. Lawler and W. Werner, The Brownian loop soup, Probab. Theory Relat. Fields 128 (2004) 565-588. Math. Review 2005f:60176
- T.M. Liggett Stochastic Interacting Systems: Contact, Voter and Exclusion Processes Springer-Verlag, Berlin, 1999 Math. Review 2001g:60247
- T.M. Liggett, R.H. Schonmann and A.M. Stacey, Domination by product measures, Ann. Probab. 25 (1997) 71-95. Math. Review 98f:60095)
- B.B.~Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, J. Fluid Mech. 62 (1974) 331-358. Math. Review number not available.
- B.B. Mandelbrot, The Fractal Geometry of Nature W.H. Freeman, San Francisco (1983) Math. Review 84h:00021
- R.W.J. Meester, Connectivity in fractal percolation, 5 (1992) 775-789 Math. Review 93m:60201
- R. Meester and R. Roy, Continuum Percolation Cambridge University Press, New York, 1996. Math. Review 98d:60193
- M.V.Menshikov, S.Yu. Popov and M. Vachkovskaia, On the connectivity properties of the complementary set in fractal percolation models, Probab. Theory Relat. Fields 119 (2001) 176-186 Math. Review 2002d:60085
- M.V.Menshikov, S.Yu. Popov and M. Vachkovskaia, On a multiscale continuous percolation model with unbounded defects, Bull. Braz. Math. Soc. 34 (2003) 417-435. Math. Review 2005c:60132
- S.~Nacu and W.~Werner, Random soups, carpets and dimensions, J. London Math. Soc. to appear (2010) Math. Review number not available.
- M.E. Orzechowski, On the Phase Transition to Sheet Percolation in Random Cantor Sets J. Stat. Phys. 82 (1996) 1081-1098 Math. Review 97e:82022
- R. Schneider and W. Weil, Stochastic and Integral Geometry Springer-Verlag, Berlin, 2008. Math. Review 2010g:60002
- S. Sheffield and W. Werner, Conformal Loop Ensembles: Construction via Loop-soups, preprint arXiv:1006.2373v1
- S. Sheffield and W. Werner, Conformal Loop Ensembles: The Markovian Characterization, preprint arXiv:1006.2374v1
- D. Stoyan, W.S. Kendall and J. Mecke, Stochastic geometry and its applications Second edition, Wiley, Chichester, 1985. Math. Review 88j:60034a
- W. Werner, SLEs as boundaries of clusters of Brownian loops, C. R. Math. Acad. Sci. Paris 337 (2003) 481-486 Math. Review 2005b:60221
- W. Werner, Some recent aspects of random conformally invariant systems, Les Houches Scool Proceedings: Session LXXXII, Mathematical Statistical Physics (2006) 57-98 Math. Review number not available.
- D.G. White, On fractal percolation in ${mathbb R}^2$, Statist. Probab. Lett. 45 (1999) 187-190 Math. Review 2000i:60117

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