Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2018-04-02T15:09:00Z No. of bitstreams: 1 AntonioDjacksonAlvesDaSilva_DISSERT.pdf: 810567 bytes, checksum: 5d6801c0f1fbf2939971f34f6f8c58a4 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2018-04-06T11:01:05Z (GMT) No. of bitstreams: 1 AntonioDjacksonAlvesDaSilva_DISSERT.pdf: 810567 bytes, checksum: 5d6801c0f1fbf2939971f34f6f8c58a4 (MD5) / Made available in DSpace on 2018-04-06T11:01:06Z (GMT). No. of bitstreams: 1 AntonioDjacksonAlvesDaSilva_DISSERT.pdf: 810567 bytes, checksum: 5d6801c0f1fbf2939971f34f6f8c58a4 (MD5) Previous issue date: 2017-07-21 / Um processo de percola??o modela o fen?meno da distribui??o ou transporte de fluidos em um meio poroso. A varia??o de um par?metro do modelo revela a exist?ncia de, geralmente, duas fases, uma fase dita subcr?tica e outra fase dita supercr?tica. Essas fases possuem caracter?sticas globais distintas e a transi??o de uma dessas fases ? outra se d? em um valor cr?tico do par?metro do modelo. O presente trabalho tem como objetivo apresentar novas demonstra??es para resultados cl?ssicos no modelo de percola??o Bernoulli de elos, a saber: o decaimento exponencial do raio de um aglomerado aberto na fase subcr?tica e a cota inferior da probabilidade de percola??o. / A percolation process models the distribution and transport of fluids in porous media. The variation of a model parameter reveals the existence of, generally, two phases, one called subcritical and the other called supercritical. These phases bear distinct global characteristics and the transition between phases takes place at a critical value for the model parameter. The present work aims at presenting new proofs for some classical results of Bond Bernoulli Percolation, namely: exponential decay of the radius of the cluster at the origin in subcritical phase and a lower bound on probability of percolation.