We study the local limit distribution of the number of occurrences of a symbol in words of length n generated at random in a regular language according to a rational stochastic model. We present an analysis of the main local limits when the finite state automaton defining the stochastic model consists of two primitive components. The limit distributions depend on several parameters and conditions, such as the main constants of mean value and variance of our statistics associated with the two components, and the existence of communications from the first to the second component. The convergence rate of these results is always of order O(n^{-1/2}). For the same statistics we also prove an analogous O(n^{-1/2}) convergence rate of the Gaussian local limit law whenever the stochastic model consists of one primitive component.
Local limit laws for symbol statistics in bicomponent rational models / M. Goldwurm, J. Lin, M. Vignati. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 970:(2023 Aug 29), pp. 114051.1-114051.18. [10.1016/j.tcs.2023.114051]
Local limit laws for symbol statistics in bicomponent rational models
M. Goldwurm
Primo
;J. LinPenultimo
;M. VignatiUltimo
2023
Abstract
We study the local limit distribution of the number of occurrences of a symbol in words of length n generated at random in a regular language according to a rational stochastic model. We present an analysis of the main local limits when the finite state automaton defining the stochastic model consists of two primitive components. The limit distributions depend on several parameters and conditions, such as the main constants of mean value and variance of our statistics associated with the two components, and the existence of communications from the first to the second component. The convergence rate of these results is always of order O(n^{-1/2}). For the same statistics we also prove an analogous O(n^{-1/2}) convergence rate of the Gaussian local limit law whenever the stochastic model consists of one primitive component.File | Dimensione | Formato | |
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