Infinite-Dimensional Functional Equations and Gaussian Limiting Distributions.
Tenth Seminar on Analysis of Algorithms
June 14, 2004 05:00 PM to 06:00 PM
Speakers:
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Abstract: |
When counting combinatorial objects which are defined recursively, this leads naturally to functional equations for the generating functions. We present several examples in combinatorial enumeration where the generating function satisfies a functional equation of the form $F(z,u)=Q(z,u,F(z,u))$. Various cases appear $F$ and $Q$ are complex valued, vector valued, or Banach space valued and similarly, the parameter $u$ may be absent, vector valued, or Banach space valued. For case, where $F$, $Q$, and $u$ are Banach space valued, we present a limit theorem for the sequence of random variables associated to the system of functional equations to a normal distribution on Banach spaces. |
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