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• R. Adamczak, B. Polaczyk, and M. Strzelecki, Modified log-Sobolev inequalities, Beckner inequalities and moment estimates, J. Func. Anal 282 (2022), no. 7.
• D. Ahlberg, E. Broman, S. Griffiths, and R. Morris, Noise sensitivity in continuum percolation, Isr. J. Math. 201 (2014), no. 2, 847–899.
• D. Ahlberg and R. Baldasso, Noise sensitivity and Voronoi percolation, Elec. J. Prob. 23 (2018).
• D. Ahlberg, V. Tassion, and A. Teixeira, Sharpness of the phase transition for continuum percolation in, Prob. Th. Rel. Fields 172 (2018), no. 1-2, 525–581.
• D. Ahlberg, V. Tassion, and A. Teixeira, Existence of an unbounded vacant set for subcritical continuum percolation, Elec. Comm. Prob. 23 (2018).
• M. Aizenman and D. J. Barsky, Sharpness of the phase transition in percolation models, Comm. Math. Phy. 108 (1987), no. 3, 489–526.
• K. S. Alexander, The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees, Ann. Appl. Prob. 6 (1996), no. 2, 466–494.
• K. S. Alexander, Boundedness of level lines for two-dimensional random fields, Ann. Prob. 24 (1996), no. 4, 1653–1674.
• V. Baumstark and G. Last, Gamma distributions for stationary Poisson flat processes, Adv. Appl. Prob. 41 (2009), 911–939.
• I. Benjamini and O. Schramm, Exceptional planes of percolation, Prob. Th. Rel. Fields 111 (1998), no. 4, 551–564.
• I. Benjamini and O. Schramm, Percolation in the hyperbolic plane, J. Am. Math. Soc. 14 (2001), no. 2, 487–507.
• I. Benjamini, G. Kalai, and O. Schramm, Noise sensitivity of Boolean functions and applications to percolation, Publ. Math. de l'IHES 90 (1999), no. 1, 5–43.
• B. Błaszczyszyn and D. Yogeshwaran, Clustering and percolation of point processes, Elec. J. Prob 18 (2013), no. 72.
• C. Bordenave, Y. Gousseau, and F. Roueff, The dead leaves model: a general tessellation modelling occlusion, Adv. Appl. Prob. 38 (2006), no. 1, 31–46.
• B. Bollobás and O. Riordan, Percolation, Cambridge University Press, 2006.
• E. Broman and R. Meester, Phase transition and uniqueness of level set percolation, J. Stat. Phys. 167 (2017), no. 6, 1376–1400.
• S. Boucheron, G. Lugosi, and P. Massart, Concentration inequalities, Oxford University Press, Oxford, 2013.
• D. Cordero-Erausquin and M. Ledoux, “Hypercontractive measures, Talagrand's inequality, and influences,” Geometric aspects of functional analysis, Springer, Berlin, Heidelberg, 2012, pp. 169–189.
• I. Derényi, G. Palla, and T. Vicsek, Clique percolation in random networks, Phy. Rev. Let 94 (2005), no. 16.
• H. Duminil-Copin and V. Tassion, A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model, Comm. Math. Phy. 343 (2016), no. 2, 725–745.
• H. Duminil-Copin, “Lectures on the Ising and Potts models on the hypercubic lattice,” Random Graphs, Phase Transitions, and the Gaussian Free Field, M. T. Barlow and G. Slade (eds.), Springer, Cham, 2017, pp. 35–161.
• H. Duminil-Copin, Introduction to Bernoulli percolation, Lecture NotesAvailable from: https://www.ihes.fr/~duminil/publi/2017percolation.pdf (2018).
• H. Duminil-Copin, A. Raoufi, and V. Tassion, Sharp phase transition for the random-cluster and Potts models via decision trees, Ann. Math. 189 (2019), no. 1, 75–99.
• H. Duminil-Copin, A. Raoufi, and V. Tassion, Exponential decay of connection probabilities for subcritical Voronoi percolation in, Prob. Th. Rel. Fields 173 (2019), no. 1-2, 479–490.
• H. Duminil-Copin, A. Raoufi, and V. Tassion, Subcritical phase of -dimensional Poisson-Boolean percolation and its vacant set, Ann. Henri Leb. 3 (2020), 677–700.
• A. Faggionato and H. A. Mimun, Connection probabilities in Poisson random graphs with uniformly bounded edges, Lat. Am. J. Probab. Math. Stat. 16 (2019), 463–486.
• C. Garban, Oded Schramm's contributions to noise sensitivity, Ann. Prob. 39 (2011), no. 5, 1702–1767.
• C. Garban and J. E. Steif, Noise Sensitivity of Boolean Functions and Percolation, Cambridge University Press, 2014.
• C. Garban and H. Vanneuville, Bargmann-Fock percolation is noise sensitive, Elec. J. Prob. 25 (2020), 1–20.
• P. P. Ghosh and R. Roy, Criticality and covered area fraction in confetti and Voronoi percolation, J. Stat. Phy. 186 (2022), no. 1, 1–26.
• E. N. Gilbert, Random plane networks, J. Soc. Ind. Appl. Math. 9 (1961), no. 4, 533–543.
• J.-B. Gouéré, Subcritical regimes in the Poisson Boolean model of continuum percolation, Ann. Prob. 36 (2008), no. 4, 1209–1220.
• J.-B. Gouéré, Percolation in a multiscale Boolean model, Lat. Am. J. Probab. Math. Stat. 11(2014), 281-297.
• J.-B. Gouéré and M. Théret, Equivalence of some subcritical properties in continuum percolation, Bernoulli 25 (2019), no. 4B, 3714–3733.
• O. Hägström, Y. Peres, and J. E. Steif, Dynamical percolation, Ann. l'Institut Henri Poincaré, Prob. et Stat 33 (1997), no. 4, 497–528.
• P. Hall, On continuum percolation, Ann. Prob. 13 (1985), no. 4, 1250–1266.
• M. Heveling and M. Reitzner, Poisson-Voronoi approximation, Ann. Appl. Prob. 19 (2019), no. 2, 719–736.
• M. Heydenreich, R. van der Hofstad, G. Last and K. Matzke. Lace expansion and mean-field behavior for the random connection model, arXiv:1908.11356, 2019.
• C. Hirsch, A Harris-Kesten theorem for confetti percolation, Rand. Struct. Alg. 47 (2015), no. 2, 361–385.
• T. Hutchcroft, New critical exponent inequalities for percolation and the random cluster model, Prob. Math. Phys. 1 (2020), no. 1, 147–165.
• S. K. Iyer and S. K. Jhawar, Phase transitions and percolation at criticality in planar enhanced random connection models, Elec. J. Prob. 26 (2021), 1–23.
• S. K. Iyer and D. Yogeshwaran, Thresholds for vanishing of ‘Isolated’ faces in random Čech and Vietoris-Rips complexes, Ann. l'Institut Henri Poincaré, Prob. et Stat 56 (2020), no. 3, 1869–1897.
• D. Jeulin, “Dead leaves models: from space tessellation to random functions,” Proc. of the Symposium on the Advances in the Theory and Applications of Random Sets (Fontainebleau, 9-11 October 1996), D. Jeulin (ed.), World Scientific Publishing Company, 1997, pp. 137–156.
• O. Kallenberg, Random Measures, Theory and Applications, Springer, Cham, 2017.
• R. Lachièze-Rey and S. Muirhead, Percolation of the excursion sets of planar symmetric shot noise fields, Stoch. Proc. Applns. 147 (2022), 175–209.
• G. Last, “Stochastic analysis for Poisson processes,” Stochastic Analysis for Poisson Point Processes, G. Peccati and M. Reitzner (eds.), Springer, Milan, 2016, pp. 1–36.
• G. Last, G. Peccati, and M. Schulte, Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization, Prob. Th. Rel. Fields 165 (2016), no. 3-4, 667–723.
• G. Last and M. Penrose, Lectures on the Poisson Process, Cambridge University Press, Cambridge, 2017.
• G. Last, G. Peccati and D. Yogeshwaran. Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees, arXiv:2101.07180, 2022.
• G. Matheron, Schéma booléen séquentiel de partitions aléatoires, Note géostatistique 89Centre de Morphologie Mathématique, Fontainebleau (1968) Available from: http://cg.ensmp.fr/bibliotheque/cgi-bin/public/bibli_index.cgi.
• R. Meester and R. Roy, Continuum percolation, Vol 119, Camridge University Press, Cambridge, 1996.
• M. V. Menshikov, Coincidence of critical points in percolation problems, Soviet Mathematics Doklady 33 (1986), 856–859.
• M. V. Menshikov, S. A. Molchanov, and A. F. Sidorenko, Percolation theory and some applications, Itogi Nauki i Tekhniki. (Series of Probability Theory, Mathematical Statistics, Theoretical Cybernetics) 24 (1986), 53–110.
• I. Molchanov, Theory of Random Sets, Springer, London, 2005.
• S. A. Molchanov and A. K. Stepanov, Percolation in random fields II, Theor. Math. Phys. 55 (1983), no. 3, 592–599.
• T. Müller, The critical probability for confetti percolation equals 1/2, Rand. Struct. Alg. 50 (2017), no. 4, 679–697.
• I. Nourdin, G. Peccati, and X. Yang, Restricted hypercontractivity on the Poisson space, Proc. Am. Math. Soc. 148 (2020), no. 8, 3617–3632.
• R. O'Donnell, Analysis of Boolean functions, Cambridge University Press, 2014.
• R. O'Donnell, “Social choice, computational complexity, Gaussian geometry, and Boolean functions,” Proceedings of the International Congress of Mathematicians – Seoul, Vol IV, Kyung Moon Sa, Seoul, 2014, pp. 633–658.
• R. O'Donnell, M. Saks, O. Schramm, and R. Servedio, Every decision tree has an influential variable FOCS, IEEE (2005), 31-39.
• G. Peccati and M. Reitzner, Eds., “Stochastic analysis for Poisson point processes: Malliavin calculus,” Wiener-Itô chaos expansions and stochastic geometry, Vol 7, Springer, Milan, 2016.
• G. Peccati and M. S. Taqqu, Wiener chaos: moments, cumulants and diagrams, Springer, 2010.
• M. D. Penrose, Non-triviality of the vacancy phase transition for the Boolean model, Elec. Comm. Prob 23 (2018).
• C. Preston, “Spatial birth-and-death processes,” Proceedings of the 40th Session of the International Statistical Institute, Vol 2, Warsaw, 1975, pp. 371–391.
• N. Privault, Laplace transform identities for the volume of stopping sets based on Poisson point processes, Adv. Appl. Prob. 47 (2015), no. 4, 919–933.
• R. Roy, The Russo-Seymour-Welsh theorem and the equality of critical densities and the “dual” critical densities for continuum percolation on, Ann. Prob 18 (1990), no. 4, 1563–75.
• R. Roy, Percolation of Poisson sticks on the plane, Prob. Th. Rel. Fields 89 (1991), no. 4, 503–517.
• Y. A. Rozanov, Markov random fields, Springer, New York, 1982.
• J. Serra, Image Analysis and Mathematical MorphologyEnglish version revised by Noel Cressie, Academic Press, Inc., London, 1982.
• O. Schramm and J. E. Steif, Quantitative noise sensitivity and exceptional times for percolation, Ann. Math. 171 (2010), 619–672.
• R. J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980.
• J. E. Steif, “A survey of dynamical percolation,” Fractal geometry and stochastics IV, Birkhäuser, Basel, 2009, pp. 145–174.
• M. Talagrand, On Russo's approximate zero-one law, Ann. Prob. 22 (1994), no. 3, 1576–1587.
• V. Tassion, Crossing probabilities for Voronoi percolation, Ann. Prob. 44 (2016), no. 5, 3385–3398.
• J. Tykesson and D. Windisch, Percolation in the vacant set of Poisson cylinders, Prob. Th. Rel. Fields 154 (2012), no. 1-2, 165–191.
• R. van Handel. Probability in High Dimension. Lecture Notes. Available from: https://web.math.princeton.edu/~rvan/APC550.pdf, 2016.
• W. Werner and E. Powell. Lectures on the Gaussian free field, arXiv:2004.04720, 2020.
• L. Wu, A new modified logarithmic Sobolev inequality for Poisson point processes and several applications, Prob. Th. Rel. Fields 118 (2000), no. 3, 427–438.
• A. Xia, “Stein's method and Poisson process approximation,” An introduction to Stein's method, Vol 4, A. D. Barbour and L. H. Y. Chen (eds.), World Scientific, Singapore, 2005, pp. 115–181.
• S. Ziesche, Sharpness of the phase transition and lower bounds for the critical intensity in continuum percolation on, Ann. l'Institut Henri Poincaré, Prob. et Stat 54 (2018), no. 2, 866–878.
• S. Zuyev, Stopping sets: gamma-type results and hitting properties, Adv. Appl. Prob. 31 (1999), no. 2, 355–366.
• S. Zuyev, Strong Markov property of Poisson processes and Slivnyak formula, Lect. Notes in Stat. 185 (2006), 77–84.