We study the maximum function of any R+-rational formal series S in two commuting variables, which assigns to every integer n is an element of 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 Theta(n(k/2)gimel(n)) for some integer k greater than or equal to -1 and some positive real lambda. 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.
On the maximum coefficients of rational formal series in commuting variables / C. CHOFFRUT, M. GOLDWURM, V. LONATI (LECTURE NOTES IN COMPUTER SCIENCE). - In: Developments in Language Theory / [a cura di] C.S. Calude, E. Calude, M.J. Dinneen. - Prima edizione. - Berlin : Springer, 2004 Dec. - ISBN 3540240144. - pp. 114-126 (( Intervento presentato al 8. convegno DLT tenutosi a Auckland nel 2004.
On the maximum coefficients of rational formal series in commuting variables
M. GOLDWURM;V. LONATI
2004
Abstract
We study the maximum function of any R+-rational formal series S in two commuting variables, which assigns to every integer n is an element of 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 Theta(n(k/2)gimel(n)) for some integer k greater than or equal to -1 and some positive real lambda. 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.File | Dimensione | Formato | |
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