References

• Aaronson, Jon; Denker, Manfred. Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps. Stoch. Dyn. 1 (2001), no. 2, 193--237. MR1840194
• Armstead, Douglas N.; Hunt, Brian R.; Ott, Edward. Anomalous diffusion in infinite horizon billiards. Phys. Rev. E (3) 67 (2003), no. 2, 021110, 7 pp. MR1974617
• Astashkin, Sergey; Sukochev, Fedor; Wong, Chin Pin. Disjointification of martingale differences and conditionally independent random variables with some applications. Studia Math. 205 (2011), no. 2, 171--200. MR2824894
• Balint, P.; Chernov, N.; Dolgopyat, D. Limit theorems for dispersing billiards with cusps. Comm. Math. Phys. 308 (2011), no. 2, 479--510. MR2851150
• Balint, P.; Chernov, N.; Dolgopyat, D. Convergence of moments for dispersing billiards with cusps, Preprint, 2013.
• Balint, Peter; Gouezel, Sebastien. Limit theorems in the stadium billiard. Comm. Math. Phys. 263 (2006), no. 2, 461--512. MR2207652
• Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. London Mathematical Society Lecture Note Series, 194. Cambridge University Press, Cambridge, 1994. viii+116 pp. ISBN: 0-521-45515-4 MR1303591
• Burkholder, D. L. Distribution function inequalities for martingales. Ann. Probability 1 (1973), 19--42. MR0365692
• Courbage, M.; Edelman, M.; Saberi Fathi, S. M.; Zaslavsky, G. M. Problem of transport in billiards with infinite horizon. Phys. Rev. E (3) 77 (2008), no. 3, 036203, 5 pp. MR2495438
• Chazottes, J.-R.; Gouezel, S. On almost-sure versions of classical limit theorems for dynamical systems. Probab. Theory Related Fields 138 (2007), no. 1-2, 195--234. MR2288069
• Chazottes, Jean-Rene; Gouezel, Sebastien. Optimal concentration inequalities for dynamical systems. Comm. Math. Phys. 316 (2012), no. 3, 843--889. MR2993935
• Jérôme Dedecker and Florence Merlevède, phMoment bounds for dependent sequences in smooth banach spaces, Preprint, 2014.
• Feller, William. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons, Inc., New York-London-Sydney 1966 xviii+636 pp. MR0210154
• Gouezel, Sebastien. Central limit theorem and stable laws for intermittent maps. Probab. Theory Related Fields 128 (2004), no. 1, 82--122. MR2027296
• Gouezel, Sebastien. Sharp polynomial estimates for the decay of correlations. Israel J. Math. 139 (2004), 29--65. MR2041223
• Gouezel, Sebastien. Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes, Ph.D. thesis, Université Paris Sud, 2004.
• Gouezel, Sebastien. Limit theorems in dynamical systems using the spectral method, preprint, 2013.
• Kato, Tosio. Perturbation theory for linear operators. Die Grundlehren der mathematischen Wissenschaften, Band 132 Springer-Verlag New York, Inc., New York 1966 xix+592 pp. MR0203473
• Liverani, Carlangelo; Saussol, Benoit; Vaienti, Sandro. A probabilistic approach to intermittency. Ergodic Theory Dynam. Systems 19 (1999), no. 3, 671--685. MR1695915
• Melbourne, Ian. Large and moderate deviations for slowly mixing dynamical systems. Proc. Amer. Math. Soc. 137 (2009), no. 5, 1735--1741. MR2470832
• Melbourne, Ian; Nicol, Matthew. Large deviations for nonuniformly hyperbolic systems. Trans. Amer. Math. Soc. 360 (2008), no. 12, 6661--6676. MR2434305
• Melbourne, Ian; Torok, Andrei. Statistical limit theorems for suspension flows. Israel J. Math. 144 (2004), 191--209. MR2121540
• Melbourne, Ian; Terhesiu, Dalia. Operator renewal theory and mixing rates for dynamical systems with infinite measure. Invent. Math. 189 (2012), no. 1, 61--110. MR2929083
• Melbourne, Ian; Torok, Andrei. Convergence of moments for axiom A and non-uniformly hyperbolic flows. Ergodic Theory Dynam. Systems 32 (2012), no. 3, 1091--1100. MR2995657
• Pomeau, Yves; Manneville, Paul. Intermittent transition to turbulence in dissipative dynamical systems. Comm. Math. Phys. 74 (1980), no. 2, 189--197. MR0576270
• Sarig, Omri. Subexponential decay of correlations. Invent. Math. 150 (2002), no. 3, 629--653. MR1946554
• Szasz, Domokos; Varju, Tamas. Limit laws and recurrence for the planar Lorentz process with infinite horizon. J. Stat. Phys. 129 (2007), no. 1, 59--80. MR2349520
• Stein, Elias M.; Weiss, Guido. Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton, N.J., 1971. x+297 pp. MR0304972
• von Bahr, Bengt; Esseen, Carl-Gustav. Inequalities for the $r$th absolute moment of a sum of random variables, $1\leq r\leq 2$. Ann. Math. Statist 36 1965 299--303. MR0170407
• Young, Lai-Sang. Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. (2) 147 (1998), no. 3, 585--650. MR1637655
• Young, Lai-Sang. Recurrence times and rates of mixing. Israel J. Math. 110 (1999), 153--188. MR1750438