{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:57Z","timestamp":1760234097399,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["439422\/2018-3","305096\/2019-2"],"award-info":[{"award-number":["439422\/2018-3","305096\/2019-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2019\/23439-4"],"award-info":[{"award-number":["2019\/23439-4"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u03d5-mixing and \u03c8-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.<\/jats:p>","DOI":"10.3390\/e23030379","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T14:08:16Z","timestamp":1616508496000},"page":"379","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Potential Well in Poincar\u00e9 Recurrence"],"prefix":"10.3390","volume":"23","author":[{"given":"Miguel","family":"Abadi","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo-USP, Rua do Mat\u00e3o, 1010 Butant\u00e3, S\u00e3o Paulo 05508-090, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5852-0031","authenticated-orcid":false,"given":"Vitor","family":"Amorim","sequence":"additional","affiliation":[{"name":"Instituto Federal de Educa\u00e7\u00e3o, Ci\u00eancia e Tecnologia de S\u00e3o Paulo-IFSP, C\u00e2mpus Araraquara, Rua Doutor Aldo Benedito Pierri, 250 Jardim Paulo Freire, Araraquara 14804-296, Brazil"}]},{"given":"Sandro","family":"Gallo","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, Universidade Federal de S\u00e3o Carlos-UFSCar, Rua dos Bem-te-vis, S\u00e3o Carlos 13565-905, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1007\/s00440-009-0221-y","article-title":"Hitting time statistics and extreme value theory","volume":"147","author":"Freitas","year":"2010","journal-title":"Probab. 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