Matching strings in encoded sequences

Author(s)

Coutinho, Adriana ^[1] ; Lambert, Rodrigo ^[2] ; Rousseau, Jerome ^{[3, 4]}

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, Sao Paulo 05508090, SP - Brazil

^[2] Univ Fed Uberlandia, Fac Matemat, Av Joao Naves de Avila 2121, Uberlandia 38408100, MG - Brazil

^[3] Univ Porto, Dept Matemat, Fac Ciencias, Rua Campo Alegre 687, Porto 4169007 - Portugal

^[4] Univ Fed Bahia, Dept Matemat, Av Ademar de Barros S-N, Salvador 40170110, BA - Brazil

• Document type: Journal article
• Source: BERNOULLI; v. 26, n. 3, p. 2021-2050, AUG 2020.
• Web of Science Citations: 0

Abstract

We investigate the length of the longest common substring for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the Renyi entropy of the source. We apply this result to the zero-inflated contamination model and the stochastic scrabble. In the case of dynamical systems, this problem is equivalent to the shortest distance between two observed orbits and its limiting relationship with the correlation dimension of the pushforward measure. An extension to the shortest distance between orbits for random dynamical systems is also provided. (AU)

• FAPESP's process: 14/19805-1 - Statistics of extreme events and dynamics of recurrence
• Grantee: Miguel Natalio Abadi
• Support Opportunities: Regular Research Grants