Padé approximants of random Stieltjes series

@article{Marklof2007PadAO,
  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},
  year={2007},
  volume={463},
  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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SHOWING 1-10 OF 40 REFERENCES
Explicit invariant measures for products of random matrices
We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL(2, C). The matrices in the product are such that one entry is
The Thouless formula for random non-Hermitian Jacobi matrices
Random non-Hermitian Jacobi matricesJn of increasing dimensionn are considered. We prove that the normalized eigenvalue counting measure ofJn converges weakly to a limiting measure μ asn→∞. We also
Iterated Random Functions
TLDR
Survey of iterated random functions offers a method for studying the steady state distribution of a Markov chain, and presents useful bounds on rates of convergence in a variety of examples.
Analytic Theory of Continued Fractions
Part I: Convergence Theory: The continued fraction as a product of linear fractional transformations Convergence theorems Convergence of continued fractions whose partial denominators are equal to
The Classical Moment Problem as a Self-Adjoint Finite Difference Operator
Abstract This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna
Noncommuting random products
Introduction. Let Xy,X2, ■■-,X„,--be a sequence of independent real valued random variables with a common distribution function F(x), and consider the sums Xy + X2 + ■■• + X„. A fundamental theorem
A Treatise on the Theory of Bessel Functions
THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression of
Markov Chains and Stochastic Stability
  • S. Meyn, R. Tweedie
  • Computer Science
    Communications and Control Engineering Series
  • 1993
TLDR
This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
Products of random matrices.
We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated
Products of Random Matrices with Applications to Schrödinger Operators
A: "Limit Theorems for Products of Random Matrices".- I - The Upper Lyapunov Exponent.- 1. Notation.- 2. The upper Lyapunov exponent.- 3. Cocycles.- 4. The theorem of Furstenberg and Kesten.- 5.
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