Journal of Statistical Physics

, Volume 136, Issue 4, pp 603–613 | Cite as

Separating Solution of a Quadratic Recurrent Equation

  • Y. G. Sinai
  • I. Vinogradov


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 fC[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→∞.


Separating solution Quadratic recurrent equation Mellin transform 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  2. 2.Landau Institute of Theoretical Physics, Russian Academy of SciencesMoscowRussia

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