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References

  1. Ben Arous, G.; Guionnet, A. Large deviations for Wigner's law and Voiculescu's non-commutative entropy. Probab. Theory Related Fields 108 (1997), no. 4, 517--542. MR1465640 (98i:15026)
  2. Bradley, Richard C. Basic properties of strong mixing conditions. A survey and some open questions. Update of, and a supplement to, the 1986 original. Probab. Surv. 2 (2005), 107--144 (electronic). MR2178042 (2006g:60054)
  3. Catoni, Olivier. Laplace transform estimates and deviation inequalities. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 1, 1--26. MR1959840 (2003m:60035)
  4. Chatterjee, S.; Dey, P.S. Applications of Stein's method for concentration inequalities. preprint, see arXiv:0906.1034v1 (2009)
  5. Dembo, A.; Guionnet, A.; Zeitouni, O. Moderate deviations for the spectral measure of certain random matrices. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 6, 1013--1042. MR2010395 (2004k:60092)
  6. Delyon, Bernard; Juditsky, c Anatoly; Liptser, Robert. Moderate deviation principle for ergodic Markov chain. Lipschitz summands. From stochastic calculus to mathematical finance, 189--209, Springer, Berlin, 2006. MR2233540 (2007b:60060)
  7. Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
  8. Eichelsbacher, Peter. Moderate and large deviations for U-processes. Stochastic Process. Appl. 74 (1998), no. 2, 273--296. MR1624408 (99c:60054)
  9. Eichelsbacher, Peter. Moderate deviations for functional U-processes. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), no. 2, 245--273. MR1819125 (2001m:60061)
  10. Eichelsbacher, Peter; Schmock, Uwe. Rank-dependent moderate deviations of U-empirical measures in strong topologies. Probab. Theory Related Fields 126 (2003), no. 1, 61--90. MR1981633 (2004b:60077)
  11. Janson, Svante. Poisson approximation for large deviations. Random Structures Algorithms 1 (1990), no. 2, 221--229. MR1138428 (93a:60041)
  12. Janson, Svante; Łuczak, Tomasz; Ruciński, Andrzej. An exponential bound for the probability of nonexistence of a specified subgraph in a random graph. Random graphs '87 (Poznań, 1987), 73--87, Wiley, Chichester, 1990. MR1094125 (91m:05168)
  13. Janson, Svante; Łuczak, Tomasz; Rucinski, Andrzej. Random graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York, 2000. xii+333 pp. ISBN: 0-471-17541-2 MR1782847 (2001k:05180)
  14. Janson, Svante; Oleszkiewicz, Krzysztof; Ruciński, Andrzej. Upper tails for subgraph counts in random graphs. Israel J. Math. 142 (2004), 61--92. MR2085711 (2005e:05126)
  15. Janson, Svante; Ruciński, Andrzej. The infamous upper tail. Probabilistic methods in combinatorial optimization. Random Structures Algorithms 20 (2002), no. 3, 317--342. MR1900611 (2003c:60013)
  16. Janson, Svante; Ruciński, Andrzej. The deletion method for upper tail estimates. Combinatorica 24 (2004), no. 4, 615--640. MR2096818 (2005i:60019)
  17. Kim, J. H.; Vu, V. H. Divide and conquer martingales and the number of triangles in a random graph. Random Structures Algorithms 24 (2004), no. 2, 166--174. MR2035874 (2005d:05135)
  18. Lee, A. J. U-statistics. Theory and practice. Statistics: Textbooks and Monographs, 110. Marcel Dekker, Inc., New York, 1990. xii+302 pp. ISBN: 0-8247-8253-4 MR1075417 (91k:60026)
  19. Nowicki, Krzysztof; Wierman, John C. Subgraph counts in random graphs using incomplete U-statistics methods. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986). Discrete Math. 72 (1988), no. 1-3, 299--310. MR0975550 (89k:05100)
  20. Ruciński, Andrzej. When are small subgraphs of a random graph normally distributed? Probab. Theory Related Fields 78 (1988), no. 1, 1--10. MR0940863 (89e:60023)
  21. Vu, Van H. A large deviation result on the number of small subgraphs of a random graph. Combin. Probab. Comput. 10 (2001), no. 1, 79--94. MR1827810 (2002d:05112)
  22. Wu, Li Ming. Moderate deviations of dependent random variables related to CLT. Ann. Probab. 23 (1995), no. 1, 420--445. MR1330777 (96f:60047)

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