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Separating Solution of a Quadratic Recurrent Equation

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Abstract

In this paper we consider the recurrent equation

$$\Lambda_{p+1}=\frac{1}{p}\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda _{q}\Lambda_{p+1-q}$$

for p≥1 with f∈C[0,1] and Λ1=y>0 given. We give conditions on f that guarantee the existence of y (0) such that the sequence Λ p with Λ1=y (0) tends to a finite positive limit as p→∞.

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References

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Authors and Affiliations

  1. Mathematics Department, Princeton University, Princeton, USA

    Y. G. Sinai & I. Vinogradov

  2. Landau Institute of Theoretical Physics, Russian Academy of Sciences, Moscow, Russia

    Y. G. Sinai

Authors
  1. Y. G. Sinai
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  2. I. Vinogradov
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Corresponding author

Correspondence to Y. G. Sinai.

Additional information

To J. Froehlich and T. Spencer with love and admiration.

The first author thanks NSF for the financial support, grant DMS N 0600996.

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Sinai, Y.G., Vinogradov, I. Separating Solution of a Quadratic Recurrent Equation. J Stat Phys 136, 603–613 (2009). https://doi.org/10.1007/s10955-009-9801-6

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  • DOI: https://doi.org/10.1007/s10955-009-9801-6

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