Pade approximants of random Stieltjes series
| Autor: | Marklof, Jens, Tourigny, Yves, Wolowski, Lech |
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| Rok vydání: | 2007 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1098/rspa.2007.0014 |
| Popis: | We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Pade approximants of the function S(t). By using the Dyson--Schmidt method for an equivalent one-dimensional disordered system, and the results of Marklof et al. (2005), we obtain explicit formulae (in terms of modified Bessel functions) for the almost-sure rate of convergence of these approximants, and for the almost-sure distribution of their poles. Comment: To appear in Proc Roy Soc |
| Databáze: | arXiv |
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