×

Large and moderate deviations for modified Engel continued fractions. (English) Zbl 1328.60074

Summary: In this paper, we consider the large and moderate deviation principles for modified Engel continued fractions, which are a representation of real numbers in number theory.

MSC:

60F10 Large deviations
11A67 Other number representations
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
Full Text: DOI

References:

[1] Dembo, A.; Zeitouni, O., Large Deviations Techniques and Applications (1998), Springer: Springer New York · Zbl 0896.60013
[2] Erdős, P.; Rényi, A.; Szüsz, P., On Engel’s and Sylvester’s series, Ann. Univ. Sci. Budapest. Eötvös. Sect. Math., 1, 7-32 (1958) · Zbl 0107.27002
[3] Fan, A.; Wang, B.; Wu, J., Arithmetic and metric properties of Oppenheim continued fraction expansions, J. Number Theory, 127, 64-82 (2007) · Zbl 1210.11086
[4] Hartono, Y.; Kraaikamp, C.; Schweiger, F., Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients, J. Théor. Nombres Bordeaux, 14, 497-516 (2002) · Zbl 1067.11042
[5] Hu, W., Moderate deviation principles for Engel’s, Sylvester’s series and Cantor’s products, Statist. Probab. Lett., 96, 247-254 (2015) · Zbl 1335.60051
[7] Rényi, A., A new approach to the theory of Engel’s series, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 5, 25-32 (1962) · Zbl 0232.10028
[8] Touchette, H., The large deviation approach to statistical mechanics, Phys. Rep., 478, 1-69 (2009)
[9] Varadhan, S. R.S., Large Deviations and Applications (1984), SIAM: SIAM Philadelphia · Zbl 0549.60023
[10] Zhu, L., On the large deviations for Engel’s, Sylvester’s series and Cantor’s products, Electron. Comm. Probab., 19, 1-9 (2014) · Zbl 1329.60060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.