Free Access
Volume 19, 2015
Page(s) 395 - 413
Published online 26 October 2015
  1. R. Arratia and S. Tavaré, Independent processes approximations for random combinatorial structures. Adv. Math. 104 (1994) 90–154. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Atlagh and M. Weber, Le théorème central limite presque sûr. Exp. Math. 18 (2000) 97–126. [Google Scholar]
  3. I. Berkes and E. Csáki, A universal result in almost sure central limit theory. Stoch. Process Appl. 94 (2001) 105–134. [CrossRef] [MathSciNet] [Google Scholar]
  4. G.A. Brosamler, An almost everywhere central limit theorem. Math. Proc. Camb. Philos Soc. 104 (1988) 561–574. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Cellarosi and Y.G. Sinai, Non-Standard Limit Theorems in Number Theory. Prokhorov and Contemporary Probability Theory. Edited by A.N. Shiryaev, S.R.S. Varadhan and E.L. Presman. Springer, Heidelberg (2013) 197–213. [Google Scholar]
  6. S. Cheng, L. Peng and L. Qi, Almost sure convergence in extreme value theory. Math. Nachr. 190 (1998) 43–50. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-M. De Koninck, I. Diouf and N. Doyon, On the truncated kernel function. J. Integer Seq. 15 (2012) Article 12.3.2. [Google Scholar]
  8. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. 2nd edition. Springer, New York (1998). [Google Scholar]
  9. K. Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude. Ark. Mat. Astron. Fys. 22 (1930) 1–14. [Google Scholar]
  10. P. Erdös and P. Turán, On some new questions on the distribution of prime numbers. Bull. Amer. Math. Soc. 54 (1948) 371–378. [CrossRef] [MathSciNet] [Google Scholar]
  11. I. Fahrner, An extension of the almost sure max-limit theorem. Stat. Probab. Lett. 49 (2000) 93–103. [CrossRef] [Google Scholar]
  12. I. Fahrner and U. Stadtmüller, On almost sure max-limit theorems. Stat. Probab. Lett. 37 (1998) 229–236. [CrossRef] [Google Scholar]
  13. A. Fisher, Convex-invariant means and a pathwise central limit theorem. Adv. Math. 63 (1987) 213–246. [CrossRef] [Google Scholar]
  14. A. Fisher, A pathwise central limit theorem for random walk. Preprint (1989). [Google Scholar]
  15. M. Ghosh, G.J. Babu and N. Mukhopadhyay, Almost sure convergence of sums of maxima and minima of positive random variables. Z. Wahrsch. Verw. Gebiete 33 (1975) 49–54. [CrossRef] [Google Scholar]
  16. R. Giuliano and C. Macci, Large deviation principles for sequences of logarithmically weighted means. J. Math. Anal. Appl. 378 (2011) 555–570. [CrossRef] [Google Scholar]
  17. D.A. Goldston, J. Pintz and C.M. Yıldırım, Primes in tuples. I. Ann. Math. 170 (2009) 819–862. [CrossRef] [Google Scholar]
  18. G.H. Hardy and E.M. Wright. An Introduction to the Theory of Numbers. 5th edition. The Clarendon Press, Oxford University Press, New York (1979). [Google Scholar]
  19. M.K. Heck, The principle of large deviations for the almost everywhere central limit theorem. Stoch. Process. Appl. 76 (1998) 61–75. [CrossRef] [Google Scholar]
  20. D. Hensley, The convolution powers of the Dickman function. J. London Math. Soc. 33 (1986) 395–406. [CrossRef] [MathSciNet] [Google Scholar]
  21. A. Hildebrand and G. Tenenbaum, Integers without large prime factors. J. Théor. Nombres Bordeaux 5 (1993) 411–484. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Hörmann, On the universal a.s. central limit theorem. Acta Math. Hung. 116 (2007) 377–398. [CrossRef] [Google Scholar]
  23. H.-K. Hwang and T.-H. Tsai, Quickselect and Dickman function. Combin. Probab. Comput. 11 (2002) 353–371. [MathSciNet] [Google Scholar]
  24. R. Kiesel and U. Stadtmüller, A large deviation principle for weighted sums of independent identically distributed random variables. J. Math. Anal. Appl. 251 (2000) 929–939. [CrossRef] [Google Scholar]
  25. M.T. Lacey and W. Philipp, A note on the almost everywhere central limit theorem. Stat. Probab. Lett. 9 (1990) 201–205. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Le Cam and G.L. Yang, Asymptotics in Statistics. Some Basic Concepts. Springer-Verlag, New York (1990). [Google Scholar]
  27. P. Lévy. Sur certain processus stochastiques homogenes. Composition Math. 7 (1939) 283–339. [Google Scholar]
  28. M.A. Lifshits and E.S. Stankevich, On the large deviation principle for the almost sure CLT. Stat. Probab. Lett. 51 (2001) 263–267. [CrossRef] [Google Scholar]
  29. M. Loève, Probability Theory I, 4th edition. Springer-Verlag, New York (1977). [Google Scholar]
  30. P. March and T. Seppäläinen, Large deviations from the almost everywhere central limit theorem. J. Theoret. Probab. 10 (1997) 935–965. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Rouault, M. Yor and M. Zani, A large deviations principle related to the strong arc-sine law. J. Theoret. Probab. 15 (2002) 793–815. [CrossRef] [MathSciNet] [Google Scholar]
  32. P. Schatte, On strong versions of the central limit theorem. Math. Nachr. 137 (1988) 249–256. [CrossRef] [MathSciNet] [Google Scholar]
  33. K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yıldırım. Bull. Amer. Math. Soc. (N.S.) 44 (2007) 1–18. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory. Translated from the second French edition by C. B. Thomas. Cambridge University Press, Cambridge (1995). [Google Scholar]
  35. A.W. van der Vaart, Asymptotic Statistics. Cambridge University Press, New York (1998). [Google Scholar]
  36. S.R.S. Varadhan, Large deviations and entropy. Entropy. Edited by A. Greven, G. Keller and G. Warnecke. Princeton University Press (2003) 199–214. [Google Scholar]
  37. E. Westzynthius, Über die Verteilung der Zahlen die zu den n ersten Primzahlen teilerfremd sind, Commun. Phys. Math. Helingsfors 5 (1931) 1–37. [Google Scholar]

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