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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Potential Well in Poincare Recurrence

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Abadi, Miguel [1] ; Amorim, Vitor [2] ; Gallo, Sandro [3]
Total Authors: 3
[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Butanta, SP - Brazil
[2] Inst Fed Educ Ciencia & Tecnol Sao Paulo IFSP, Campus Araraquara, BR-14804296 Araraquara, SP - Brazil
[3] Univ Fed Sao Carlos UFSCar, Dept Estat, Rua Bem Te Vis, BR-13565905 Sao Carlos - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Entropy; v. 23, n. 3 MAR 2021.
Web of Science Citations: 0

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For phi-mixing and psi-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar. (AU)

FAPESP's process: 19/23439-4 - Stochastic chains with unbounded memory and random walks on graphs
Grantee:Alexsandro Giacomo Grimbert Gallo
Support Opportunities: Regular Research Grants