Scaling in simple continued fraction
| Autor: | Yadav, Avinash Chand |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/ab6513 |
| Popis: | We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0, x_1, x_2, \dots x_n\}$, where $x$'s are the continued fraction elements computed with an exact value of $\pi$ up to $N$ precision. We numerically compute probability distribution for the elements and observe a striking power-law behavior $P(x)\sim x^{-2}$. The statistical analysis indicates that the elements are uncorrelated and the scaling is robust with respect to the precision. Our arguments reveal that the underlying mechanism generating such a scaling may be sample space reducing process. Comment: 5 pages, 5 figures |
| Databáze: | arXiv |
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