Abstract
One goal of this paper is to prove that dynamical critical site percolation on the planar triangular lattice has exceptional times at which percolation occurs. In doing so, new quantitative noise sensitivity results for percolation are obtained. The latter is based on a novel method for controlling the “level $k$” Fourier coefficients via the construction of a randomized algorithm which looks at random bits, outputs the value of a particular function but looks at any fixed input bit with low probability. We also obtain upper and lower bounds on the Hausdorff dimension of the set of percolating times. We then study the problem of exceptional times for certain “$k$arm” events on wedges and cones. As a corollary of this analysis, we prove, among other things, that there are no times at which there are two infinite “white” clusters, obtain an upper bound on the Hausdorff dimension of the set of times at which there are both an infinite white cluster and an infinite black cluster and prove that for dynamical critical bond percolation on the square grid there are no exceptional times at which three disjoint infinite clusters are present.

[ADA] M. Aizenman, S. Duplantier, and A. Aharony, "Connectivity exponents and external perimeter in 2D percolation models," Phys. Rev. Lett., vol. 83, pp. 13591362, 1999.
@article{ADA,
author={Aizenman, M. and Duplantier, S. and Aharony, A.},
TITLE={Connectivity exponents and external perimeter in 2D percolation models},
JOURNAL={Phys. Rev. Lett.},
VOLUME={83},
YEAR={1999},
PAGES={13591362},
} 
[BKS] I. Benjamini, G. Kalai, and O. Schramm, "Noise sensitivity of Boolean functions and applications to percolation," Inst. Hautes Études Sci. Publ. Math., iss. 90, pp. 543 (2001), 1999.
@article {BKS, MRKEY = {1813223},
AUTHOR = {Benjamini, Itai and Kalai, Gil and Schramm, Oded},
TITLE = {Noise sensitivity of {B}oolean functions and applications to percolation},
JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
NUMBER = {90},
YEAR = {1999},
PAGES = {543 (2001)},
ISSN = {00738301},
CODEN = {PMIHA6},
MRCLASS = {60B15 (60K35 68Q15 82B43 94C10)},
MRNUMBER = {2001m:60016},
MRREVIEWER = {H. Kesten},
URL = {http://www.numdam.org/item?id=PMIHES_1999__90__5_0},
ZBLNUMBER = {0986.60002},
} 
[BeSc] I. Benjamini and O. Schramm, "Exceptional planes of percolation," Probab. Theory Related Fields, vol. 111, iss. 4, pp. 551564, 1998.
@article {BeSc, MRKEY = {1641830},
AUTHOR = {Benjamini, Itai and Schramm, Oded},
TITLE = {Exceptional planes of percolation},
JOURNAL = {Probab. Theory Related Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {111},
YEAR = {1998},
NUMBER = {4},
PAGES = {551564},
ISSN = {01788051},
CODEN = {PTRFEU},
MRCLASS = {60K35 (82B43)},
MRNUMBER = {99i:60173},
MRREVIEWER = {Ronald Meester},
DOI = {10.1007/s004400050177},
ZBLNUMBER = {0910.60076},
} 
[BSW] I. Benjamini, O. Schramm, and D. B. Wilson, "Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read," in STOC’05: Proc. 37th Annual ACM Symposium on Theory of Computing, New York: ACM, 2005, pp. 244250.
@incollection {BSW, MRKEY = {2181623},
AUTHOR = {Benjamini, Itai and Schramm, Oded and Wilson, David B.},
TITLE = {Balanced {B}oolean functions that can be evaluated so that every input bit is unlikely to be read},
BOOKTITLE = {{\rm S{TOC}'05}: {P}roc. 37th {A}nnual {\rm ACM} {S}ymposium on {T}heory of {C}omputing},
PAGES = {244250},
PUBLISHER = {ACM},
ADDRESS = {New York},
YEAR = {2005},
MRCLASS = {68W20 (06E30)},
MRNUMBER = {2006g:68280},
} 
[BMW] J. van den Berg, R. Meester, and D. G. White, "Dynamic Boolean models," Stochastic Process. Appl., vol. 69, iss. 2, pp. 247257, 1997.
@article {BMW, MRKEY = {1472953},
AUTHOR = {Berg, {J. van den} and Meester, Ronald and White, Damien G.},
TITLE = {Dynamic {B}oolean models},
JOURNAL = {Stochastic Process. Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {69},
YEAR = {1997},
NUMBER = {2},
PAGES = {247257},
ISSN = {03044149},
CODEN = {STOPB7},
MRCLASS = {60K35 (82C43)},
MRNUMBER = {98j:60134},
MRREVIEWER = {Olle H{ä}ggstr{ö}m},
DOI = {10.1016/S03044149(97)000446},
ZBLNUMBER = {0911.60083},
} 
[BrSt] E. I. Broman and J. E. Steif, "Dynamical stability of percolation for some interacting particle systems and $\epsilon$movability," Ann. Probab., vol. 34, iss. 2, pp. 539576, 2006.
@article {BrSt, MRKEY = {2223951},
AUTHOR = {Broman, Erik I. and Steif, Jeffrey E.},
TITLE = {Dynamical stability of percolation for some interacting particle systems and {$\epsilon$}movability},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {34},
YEAR = {2006},
NUMBER = {2},
PAGES = {539576},
ISSN = {00911798},
CODEN = {APBYAE},
MRCLASS = {60K35 (82B43 82C43)},
MRNUMBER = {2007b:60233},
MRREVIEWER = {B. M. Gurevich},
DOI = {10.1214/009117905000000602},
ZBLNUMBER = {1107.82058},
} 
[CN] F. Camia and C. M. Newman, "Twodimensional critical percolation: the full scaling limit," Comm. Math. Phys., vol. 268, iss. 1, pp. 138, 2006.
@article {CN, MRKEY = {2249794},
AUTHOR = {Camia, Federico and Newman, Charles M.},
TITLE = {Twodimensional critical percolation: the full scaling limit},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {268},
YEAR = {2006},
NUMBER = {1},
PAGES = {138},
ISSN = {00103616},
CODEN = {CMPHAY},
MRCLASS = {82B43 (60K35)},
MRNUMBER = {2007m:82032},
MRREVIEWER = {Christophe Garban},
DOI = {10.1007/s0022000600861},
ZBLNUMBER = {1117.60086},
} 
[Diestel] R. Diestel, Graph Theory, New York: SpringerVerlag, 1997.
@book {Diestel, MRKEY = {1448665},
AUTHOR = {Diestel, Reinhard},
TITLE = {Graph Theory},
SERIES = {Grad. Texts Math.},
NUMBER = {173},
PUBLISHER = {SpringerVerlag},
ADDRESS = {New York},
YEAR = {1997},
PAGES = {xiv+289},
ISBN = {0387982108},
MRCLASS = {0501},
MRNUMBER = {1448665},
ZBLNUMBER={1086.05001},
} 
[Eva89] S. N. Evans, "Local properties of Lévy processes on a totally disconnected group," J. Theoret. Probab., vol. 2, iss. 2, pp. 209259, 1989.
@article {Eva89, MRKEY = {987578},
AUTHOR = {Evans, Steven N.},
TITLE = {Local properties of {L}évy processes on a totally disconnected group},
JOURNAL = {J. Theoret. Probab.},
FJOURNAL = {Journal of Theoretical Probability},
VOLUME = {2},
YEAR = {1989},
NUMBER = {2},
PAGES = {209259},
ISSN = {08949840},
CODEN = {JTPREO},
MRCLASS = {60J30 (60G17)},
MRNUMBER = {90g:60069},
MRREVIEWER = {Bert Fristedt},
DOI = {10.1007/BF01053411},
ZBLNUMBER = {0683.60010},
} 
[FG] P. J. Fitzsimmons and R. K. Getoor, "On the potential theory of symmetric Markov processes," Math. Ann., vol. 281, iss. 3, pp. 495512, 1988.
@article {FG, MRKEY = {954155},
AUTHOR = {Fitzsimmons, P. J. and Getoor, R. K.},
TITLE = {On the potential theory of symmetric {M}arkov processes},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {281},
YEAR = {1988},
NUMBER = {3},
PAGES = {495512},
ISSN = {00255831},
CODEN = {MAANA},
MRCLASS = {60J45},
MRNUMBER = {89k:60110},
MRREVIEWER = {Jutta Steffens},
DOI = {10.1007/BF01457159},
ZBLNUMBER = {0627.60067},
} 
[GS] R. K. Getoor and M. J. Sharpe, "Naturality, standardness, and weak duality for Markov processes," Z. Wahrsch. Verw. Gebiete, vol. 67, iss. 1, pp. 162, 1984.
@article {GS, MRKEY = {756804},
AUTHOR = {Getoor, R. K. and Sharpe, M. J.},
TITLE = {Naturality, standardness, and weak duality for {M}arkov processes},
JOURNAL = {Z. Wahrsch. Verw. Gebiete},
FJOURNAL = {Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete},
VOLUME = {67},
YEAR = {1984},
NUMBER = {1},
PAGES = {162},
ISSN = {00443719},
CODEN = {ZWVGAA},
MRCLASS = {60J45 (60J25)},
MRNUMBER = {86f:60093},
MRREVIEWER = {J. Walsh},
DOI = {10.1007/BF00534082},
ZBLNUMBER = {0553.60070},
} 
[Grimmett] G. Grimmett, Percolation, Second ed., New York: SpringerVerlag, 1999.
@book {Grimmett, MRKEY = {1707339},
AUTHOR = {Grimmett, Geoffrey},
TITLE = {Percolation},
SERIES = {Grundl. Math. Wissen.},
NUMBER = {321},
EDITION = {Second},
PUBLISHER = {SpringerVerlag},
ADDRESS = {New York},
YEAR = {1999},
PAGES = {xiv+444},
ISBN = {3540649026},
MRCLASS = {60K35 (6002 82B43)},
MRNUMBER = {2001a:60114},
MRREVIEWER = {Neal Madras},
} 
[HPS] O. Häggström, Y. Peres, and J. E. Steif, "Dynamical percolation," Ann. Inst. H. Poincaré Probab. Statist., vol. 33, iss. 4, pp. 497528, 1997.
@article {HPS, MRKEY = {1465800},
AUTHOR = {H{ä}ggstr{ö}m, Olle and Peres, Yuval and Steif, Jeffrey E.},
TITLE = {Dynamical percolation},
JOURNAL = {Ann. Inst. H. Poincaré Probab. Statist.},
FJOURNAL = {Annales de l'Institut Henri Poincaré. Probabilités et Statistiques},
VOLUME = {33},
YEAR = {1997},
NUMBER = {4},
PAGES = {497528},
ISSN = {02460203},
CODEN = {AHPBAR},
MRCLASS = {60K35 (82C43)},
MRNUMBER = {98m:60153},
MRREVIEWER = {H. Kesten},
DOI = {10.1016/S02460203(97)801033},
} 
[HS] T. Hara and G. Slade, "Meanfield behaviour and the lace expansion," in Probability and Phase Transition (Cambridge, 1993), Dordrecht: Kluwer Acad. Publ., 1994, pp. 87122.
@incollection {HS, MRKEY = {1283177},
AUTHOR = {Hara, Takashi and Slade, Gordon},
TITLE = {Meanfield behaviour and the lace expansion},
BOOKTITLE = {Probability and Phase Transition ({C}ambridge, 1993)},
SERIES = {% Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
NUMBER = {420},
PAGES = {87122},
PUBLISHER = {Kluwer Acad. Publ.},
ADDRESS = {Dordrecht},
YEAR = {1994},
MRCLASS = {82B41 (60K35 8202 82B43)},
MRNUMBER = {95d:82033},
MRREVIEWER = {Neal Madras},
ZBLNUMBER = {0831.60107},
} 
[Harris] T. E. Harris, "A lower bound for the critical probability in a certain percolation process," Proc. Cambridge Philos. Soc., vol. 56, pp. 1320, 1960.
@article {Harris, MRKEY = {0115221},
AUTHOR = {Harris, T. E.},
TITLE = {A lower bound for the critical probability in a certain percolation process},
JOURNAL = {Proc. Cambridge Philos. Soc.},
VOLUME = {56},
YEAR = {1960},
PAGES = {1320},
MRCLASS = {60.00},
MRNUMBER = {22 \#6023},
MRREVIEWER = {G. Newell},
ZBLNUMBER = {0122.36403},
} 
[Haw84] J. Hawkes, "Some geometric aspects of potential theory," in Stochastic Analysis and Applications (Swansea, 1983), New York: SpringerVerlag, 1984, pp. 130154.
@incollection {Haw84, MRKEY = {777518},
AUTHOR = {Hawkes, John},
TITLE = {Some geometric aspects of potential theory},
BOOKTITLE = {Stochastic Analysis and Applications ({S}wansea, 1983)},
SERIES = {Lecture Notes in Math.},
NUMBER = {1095},
PAGES = {130154},
PUBLISHER = {SpringerVerlag},
ADDRESS = {New York},
YEAR = {1984},
MRCLASS = {60J45 (60J30)},
MRNUMBER = {86h:60146},
MRREVIEWER = {Mamoru Kanda},
ZBLNUMBER = {0558.60055},
} 
[Kahane] J. Kahane, Some Random Series of Functions, Second ed., Cambridge: Cambridge Univ. Press, 1985.
@book {Kahane, MRKEY = {833073},
AUTHOR = {Kahane, JeanPierre},
TITLE = {Some Random Series of Functions},
SERIES = {Cambridge Studies Adv. Mat.},
NUMBER = {5},
EDITION = {Second},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1985},
PAGES = {xiv+305},
ISBN = {052124966X; 0521456029},
MRCLASS = {60G99 (42A61 60G15 60G17)},
MRNUMBER = {87m:60119},
MRREVIEWER = {Michael Marcus},
ZBLNUMBER = {0571.60002},
} 
[Kesten] H. Kesten, Percolation Theory for Mathematicians, Mass.: Birkhäuser, 1982.
@book {Kesten, MRKEY = {692943},
AUTHOR = {Kesten, Harry},
TITLE = {Percolation Theory for Mathematicians},
SERIES = {Progr. Prob. Statist.},
NUMBER = {2},
PUBLISHER = {Birkhäuser},
ADDRESS = {Mass.},
YEAR = {1982},
PAGES = {iv+423},
ISBN = {3764331070},
MRCLASS = {60K35 (05C70 82A43)},
MRNUMBER = {84i:60145},
MRREVIEWER = {R. T. Smythe},
ZBLNUMBER = {0522.60097},
} 
[K2] H. Kesten, "Scaling relations for $2$Dpercolation," Comm. Math. Phys., vol. 109, iss. 1, pp. 109156, 1987.
@article {K2, MRKEY = {879034},
AUTHOR = {Kesten, Harry},
TITLE = {Scaling relations for {$2$}{D}percolation},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {109},
YEAR = {1987},
NUMBER = {1},
PAGES = {109156},
ISSN = {00103616},
CODEN = {CMPHAY},
MRCLASS = {60K35 (82A43)},
MRNUMBER = {88k:60174},
MRREVIEWER = {R. T. Smythe},
URL = {http://projecteuclid.org/getRecord?id=euclid.cmp/1104116714},
} 
[KSZ] H. Kesten, V. Sidoravicius, and Y. Zhang, "Almost all words are seen in critical site percolation on the triangular lattice," Electron. J. Probab., vol. 3, p. 10, 1998.
@article {KSZ, MRKEY = {1637089},
AUTHOR = {Kesten, Harry and Sidoravicius, V. and Zhang, Y.},
TITLE = {Almost all words are seen in critical site percolation on the triangular lattice},
JOURNAL = {Electron. J. Probab.},
FJOURNAL = {Electronic Journal of Probability},
VOLUME = {3},
YEAR = {1998},
PAGES = {no. 10, 75 pp.},
ISSN = {10836489},
MRCLASS = {60K35},
MRNUMBER = {99j:60155},
MRREVIEWER = {Rahul Roy},
URL = {http://www.math.washington.edu/~ejpecp/EjpVol3/paper10.abs.html},
ZBLNUMBER={0908.60082},
} 
[KZ] H. Kesten and Y. Zhang, "Strict inequalities for some critical exponents in twodimensional percolation," J. Statist. Phys., vol. 46, iss. 56, pp. 10311055, 1987.
@article {KZ, MRKEY = {893131},
AUTHOR = {Kesten, Harry and Zhang, Yu},
TITLE = {Strict inequalities for some critical exponents in twodimensional percolation},
JOURNAL = {J. Statist. Phys.},
FJOURNAL = {Journal of Statistical Physics},
VOLUME = {46},
YEAR = {1987},
NUMBER = {56},
PAGES = {10311055},
ISSN = {00224715},
CODEN = {JSTPSB},
MRCLASS = {60K35 (82A43)},
MRNUMBER = {89g:60305},
MRREVIEWER = {John C. Wierman},
ZBLNUMBER = {0683.60081},
} 
[Lawler] G. F. Lawler, Conformally Invariant Processes in the Plane, Providence, RI: Amer. Math. Soc., 2005.
@book {Lawler, MRKEY = {2129588},
AUTHOR = {Lawler, Gregory F.},
TITLE = {Conformally Invariant Processes in the Plane},
SERIES = {Math. Surveys Monogr.},
NUMBER = {114},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2005},
PAGES = {xii+242},
ISBN = {0821836773},
MRCLASS = {6002 (3002 30C35 31A15 60J65 81T40 82B27)},
MRNUMBER = {2006i:60003},
MRREVIEWER = {ZhenQing Chen},
ZBLNUMBER = {1074.60002},
} 
[LSW] G. F. Lawler, O. Schramm, and W. Werner, "Onearm exponent for critical 2D percolation," Electron. J. Probab., vol. 7, p. 13, 2002.
@article {LSW, MRKEY = {1887622},
AUTHOR = {Lawler, Gregory F. and Schramm, Oded and Werner, Wendelin},
TITLE = {Onearm exponent for critical 2{D} percolation},
JOURNAL = {Electron. J. Probab.},
FJOURNAL = {Electronic Journal of Probability},
VOLUME = {7},
YEAR = {2002},
PAGES = {13 pp.},
ISSN = {10836489},
MRCLASS = {60K35 (82B43)},
MRNUMBER = {2002k:60204},
MRREVIEWER = {Rapha{ë}l Cerf},
URL = {http://www.math.washington.edu/~ejpecp/EjpVol7/paper2.abs.html},
ZBLNUMBER={1015.60091},
} 
[LSWup2] G. F. Lawler, O. Schramm, and W. Werner, "Sharp estimates for Brownian nonintersection probabilities," in In and Out of Equilibrium (Mambucaba, 2000), Boston, MA: Birkhäuser, 2002, pp. 113131.
@incollection {LSWup2, MRKEY = {1901950},
AUTHOR = {Lawler, Gregory F. and Schramm, Oded and Werner, Wendelin},
TITLE = {Sharp estimates for {B}rownian nonintersection probabilities},
BOOKTITLE = {In and Out of Equilibrium ({M}ambucaba, 2000)},
SERIES = {Progr. Probab.},
NUMBER = {51},
PAGES = {113131},
PUBLISHER = {Birkhäuser},
ADDRESS = {Boston, MA},
YEAR = {2002},
MRCLASS = {60J65},
MRNUMBER = {2003d:60162},
MRREVIEWER = {Peter M{ö}rters},
ZBLNUMBER = {1011.60062},
} 
[PSSW] Y. Peres, O. Schramm, S. Sheffield, and D. B. Wilson, "Randomturn hex and other selection games," Amer. Math. Monthly, vol. 114, iss. 5, pp. 373387, 2007.
@article {PSSW, MRKEY = {2309980},
AUTHOR = {Peres, Yuval and Schramm, Oded and Sheffield, Scott and Wilson, David B.},
TITLE = {Randomturn hex and other selection games},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {114},
YEAR = {2007},
NUMBER = {5},
PAGES = {373387},
ISSN = {00029890},
CODEN = {AMMYAE},
MRCLASS = {91A46 (00A08 60C05)},
MRNUMBER = {2008a:91039},
MRREVIEWER = {G. A. Heuer},
ZBLNUMBER = {1153.91012},
} 
[PS] Y. Peres and J. E. Steif, "The number of infinite clusters in dynamical percolation," Probab. Theory Related Fields, vol. 111, iss. 1, pp. 141165, 1998.
@article {PS, MRKEY = {1626782},
AUTHOR = {Peres, Yuval and Steif, Jeffrey E.},
TITLE = {The number of infinite clusters in dynamical percolation},
JOURNAL = {Probab. Theory Related Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {111},
YEAR = {1998},
NUMBER = {1},
PAGES = {141165},
ISSN = {01788051},
CODEN = {PTRFEU},
MRCLASS = {60K35 (31C15 82C43)},
MRNUMBER = {99e:60217},
MRREVIEWER = {H. Kesten},
DOI = {10.1007/s004400050165},
ZBLNUMBER = {0906.60069},
} 
[Reimer] D. Reimer, "Proof of the van den BergKesten conjecture," Combin. Probab. Comput., vol. 9, iss. 1, pp. 2732, 2000.
@article {Reimer, MRKEY = {1751301},
AUTHOR = {Reimer, David},
TITLE = {Proof of the van den {B}erg{K}esten conjecture},
JOURNAL = {Combin. Probab. Comput.},
FJOURNAL = {Combinatorics, Probability and Computing},
VOLUME = {9},
YEAR = {2000},
NUMBER = {1},
PAGES = {2732},
ISSN = {09635483},
MRCLASS = {60C05 (60E15 60K35)},
MRNUMBER = {2001g:60017},
MRREVIEWER = {H. Kesten},
DOI = {10.1017/S0963548399004113},
ZBLNUMBER = {0947.60093},
} 
[Schramm] O. Schramm, "Scaling limits of looperased random walks and uniform spanning trees," Israel J. Math., vol. 118, pp. 221288, 2000.
@article {Schramm, MRKEY = {1776084},
AUTHOR = {Schramm, Oded},
TITLE = {Scaling limits of looperased random walks and uniform spanning trees},
JOURNAL = {Israel J. Math.},
FJOURNAL = {Israel Journal of Mathematics},
VOLUME = {118},
YEAR = {2000},
PAGES = {221288},
ISSN = {00212172},
CODEN = {ISJMAP},
MRCLASS = {60K35 (30C85 60H15 82B27 82B44)},
MRNUMBER = {2001m:60227},
MRREVIEWER = {Almut Burchard},
DOI = {10.1007/BF02803524},
ZBLNUMBER = {0968.60093},
} 
[Smirnov] S. Smirnov, "Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits," C. R. Acad. Sci. Paris Sér. I Math., vol. 333, iss. 3, pp. 239244, 2001.
@article {Smirnov, MRKEY = {1851632},
AUTHOR = {Smirnov, Stanislav},
TITLE = {Critical percolation in the plane: conformal invariance, {C}ardy's formula, scaling limits},
JOURNAL = {C. R. Acad. Sci. Paris Sér. I Math.},
FJOURNAL = {Comptes Rendus de l'Académie des Sciences. Série I. Mathématique},
VOLUME = {333},
YEAR = {2001},
NUMBER = {3},
PAGES = {239244},
ISSN = {07644442},
CODEN = {CASMEI},
MRCLASS = {60K35 (82B43)},
MRNUMBER = {2002f:60193},
DOI = {10.1016/S07644442(01)019917},
ZBLNUMBER = {0985.60090},
} 
[Smirnov1] S. Smirnov, Critical percolation in the plane. I. Conformal invariance and Cardy’s formula, II. Continuum scaling limit (long version).
@misc{Smirnov1,
author={Smirnov, S},
TITLE={Critical percolation in the plane. I. Conformal invariance and Cardy's formula, II. Continuum scaling limit (long version)},
NOTE={preprint},
ARXIV={0909.4499},
} 
[SW] S. Smirnov and W. Werner, "Critical exponents for twodimensional percolation," Math. Res. Lett., vol. 8, iss. 56, pp. 729744, 2001.
@article {SW, MRKEY = {1879816},
AUTHOR = {Smirnov, Stanislav and Werner, Wendelin},
TITLE = {Critical exponents for twodimensional percolation},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {8},
YEAR = {2001},
NUMBER = {56},
PAGES = {729744},
ISSN = {10732780},
MRCLASS = {60K35},
MRNUMBER = {2003i:60173},
ZBLNUMBER = {1009.60087},
} 
[Talagrand] M. Talagrand, "Concentration of measure and isoperimetric inequalities in product spaces," Inst. Hautes Études Sci. Publ. Math., iss. 81, pp. 73205, 1995.
@article {Talagrand, MRKEY = {1361756},
AUTHOR = {Talagrand, Michel},
TITLE = {Concentration of measure and isoperimetric inequalities in product spaces},
JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
NUMBER = {81},
YEAR = {1995},
PAGES = {73205},
ISSN = {00738301},
CODEN = {PMIHA6},
MRCLASS = {60E15 (60D05)},
MRNUMBER = {97h:60016},
MRREVIEWER = {G. Schechtman},
URL = {http://www.numdam.org/item?id=PMIHES_1995__81__73_0},
ZBLNUMBER = {0864.60013},
}