Padé approximants of random Stieltjes series

  title={Pad{\'e} approximants of random Stieltjes series},
  author={Jens Marklof and Yves Tourigny and Lech Wołowski},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  pages={2813 - 2832}
We consider the random continued fractionwhere sn are independent random variables with the same gamma distribution. Every realization of the sequence defines a Stieltjes function that can be expressed asfor some measure σ on the positive half-line. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Padé approximants of the function S. Using the Dyson–Schmidt method for an equivalent one-dimensional disordered system and the results of… 

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