We present a non-Gaussian local limit theorem for the number of occurrences of a given symbol in a word of length n generated at random. The stochastic model for the random generation is defined by a rational formal series with non-negative real coefficients. The result yields a local limit towards a uniform density function and holds under the assumption that the formal series defining the model is recognized by a weighted finite state automaton with two primitive components having equal dominant eigenvalue.
CITATION STYLE
Goldwurm, M., Lin, J., & Vignati, M. (2018). A local limit property for pattern statistics in bicomponent stochastic models. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10952 LNCS, pp. 114–125). Springer Verlag. https://doi.org/10.1007/978-3-319-94631-3_10
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