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2004

On the Maximum Coefficients of Rational Formal Series in Commuting Variables

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On the Maximum Coefficients of Rational Formal Series in Commuting Variables
We study the maximum function of any R+-rational formal series S in two commuting variables, which assigns to every integer n N, the maximum coefficient of the monomials of degree n. We show that if S is a power of any primitive rational formal series, then its maximum function is of the order (nk/2 n ) for some integer k -1 and some positive real . Our analysis is related to the study of limit distributions in pattern statistics. In particular, we prove a general criterion for establishing Gaussian local limit laws for sequences of discrete positive random variables.
Christian Choffrut, Massimiliano Goldwurm, Violett
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2004
Where DLT
Authors Christian Choffrut, Massimiliano Goldwurm, Violetta Lonati
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