{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T14:16:30Z","timestamp":1780064190918,"version":"3.54.0"},"reference-count":49,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,1]],"date-time":"2017-04-01T00:00:00Z","timestamp":1491004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A nonlinear random walk related to the porous medium equation (nonlinear Fokker\u2013Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution (     G  q , \u03b2    ( x )  \u221d   [ 1 \u2212  ( 1 \u2212 q )  \u03b2  x 2  ]   1 \/ ( 1 \u2212 q )      ), which is a solution of the porous medium equation. This can be seen as a verification of a generalized central limit theorem where the attractor is a q-Gaussian distribution, reducing to the Gaussian one when the linearity is recovered (    q \u2192 1    ). In addition, motivated by this random walk, a nonlinear Markov chain is suggested.<\/jats:p>","DOI":"10.3390\/e19040155","type":"journal-article","created":{"date-parts":[[2017,4,3]],"date-time":"2017-04-03T13:32:30Z","timestamp":1491226350000},"page":"155","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Random Walks Associated with Nonlinear Fokker\u2013Planck Equations"],"prefix":"10.3390","volume":"19","author":[{"given":"Renio","family":"Dos Santos Mendes","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, Maring\u00e1 87020-900, Brazil"},{"name":"National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ervin","family":"Lenzi","sequence":"additional","affiliation":[{"name":"National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil"},{"name":"Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Av. General Carlos Cavalcanti 4748, Ponta Grossa 84030-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis","family":"Malacarne","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, Maring\u00e1 87020-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergio","family":"Picoli","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, Maring\u00e1 87020-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Max","family":"Jauregui","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, Maring\u00e1 87020-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,1]]},"reference":[{"key":"ref_1","unstructured":"Einstein, A. 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