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2006

Local Limit Properties for Pattern Statistics and Rational Models

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Local Limit Properties for Pattern Statistics and Rational Models
Motivated by problems of pattern statistics, we study the limit distribution of the random variable counting the number of occurrences of the symbol a in a word of length n chosen at random in {a, b} , according to a probability distribution defined via a rational formal series s with positive real coefficients. Our main result is a local limit theorem of Gaussian type for these statistics under the hypothesis that s is a power of a primitive series. This result is obtained by showing a general criterion for (Gaussian) local limit laws of sequences of integer random variables. To prove our result we also introduce and analyze a notion of symbol-periodicity for irreducible matrices, whose entries are polynomials over positive semirings; the properties we prove on this topic extend the classical Perron
Alberto Bertoni, Christian Choffrut, Massimiliano
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2006
Where MST
Authors Alberto Bertoni, Christian Choffrut, Massimiliano Goldwurm, Violetta Lonati
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