A Local Limit Property for Pattern Statistics in Bicomponent Stochastic Models

Abstract : 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.
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Massimiliano Goldwurm, Jianyi Lin, Marco Vignati. A Local Limit Property for Pattern Statistics in Bicomponent Stochastic Models. 20th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2018, Halifax, NS, Canada. pp.114-125, ⟨10.1007/978-3-319-94631-3_10⟩. ⟨hal-01905636⟩

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