{"id":299,"date":"2024-09-18T18:45:18","date_gmt":"2024-09-18T18:45:18","guid":{"rendered":"http:\/\/localhost:8000\/?page_id=299"},"modified":"2024-09-18T19:03:50","modified_gmt":"2024-09-18T19:03:50","slug":"seminarios-de-probabilidade-2017","status":"publish","type":"page","link":"https:\/\/ppge.im.ufrj.br\/en\/seminarios-de-probabilidade-2017\/","title":{"rendered":"Semin\u00e1rios de probabilidade \u2013 2017"},"content":{"rendered":"

Semin\u00e1rios de probabilidade \u2013 2017<\/h2><\/div>
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Coordena\u00e7\u00e3o:\u00a0<\/strong>Professora Maria Eulalia Vares<\/p>\n

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As palestras ocorrerem na sala C-119 nas segundas-feiras as 15h30, a menos de algumas exce\u00e7\u00f5es devidamente indicadas.<\/p>\n<\/div>\n<\/div>\n<\/div>

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Lista completa<\/strong><\/p>\n<\/div>

<\/i><\/i><\/span>27\/11
\nProcesso de exclus\u00e3o com taxa lenta na fronteira<\/em>
\nAdriana Neumann de Oliveira (UFRGS)<\/span><\/a><\/h4><\/div>
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Nesta palestra falarei sobre o processo de exclus\u00e3o com taxa lenta na <\/span><\/a>fronteira, que s\u00e3o part\u00edculas que movem-se em como passeios aleat\u00f3rios independentes exceto pela regra de exclus\u00e3o que pro\u00edbe duas ou mais part\u00edculas de ocuparem o mesmo s\u00edtio ao mesmo tempo. Al\u00e9m disso, nos s\u00edtios 1 e n-1 pode ser adicionada ou retirada uma part\u00edcula (sempre respeitando a regra de exclus\u00e3o) com taxa proporcional a n^, onde a \u00e9 uma constante n\u00e3o-negativa.<\/div>\n
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Este modelo e outros semelhantes a ele v\u00eam sendo muito estudados, pois despertam interesse pela sua aplicabilidade e pela sua parte te\u00f3rica.
\nO interesse na aplicabilidade \u00e9 devido ao fato de que ele modela a transfer\u00eancia de massa entre reservat\u00f3rios com diferentes densidades. E, uma das suas n\u00e3o trivialidades te\u00f3ricas, por exemplo, \u00e9 fato da medida invariante ser dada atrav\u00e9s de matrizes de Ansatz. Outro aspecto te\u00f3rico interessante, \u00e9 que o limite hidrodin\u00e2mico \u00e9 dado pela equa\u00e7\u00e3o do calor com condi\u00e7\u00f5es de fronteira que dependem de qu\u00e3o lenta \u00e9 o nascimento e morte de part\u00edculas na fronteira. Essas condi\u00e7\u00f5es de fronteira sofrem uma transi\u00e7\u00e3o de fase: se a em [0,1), temos Dirichlet; para a>1, temos Neumann e para o caso cr\u00edtico a=1, temos Robin. Nesta palestra, al\u00e9m do limite hidrodin\u00e2mico, ser\u00e3o apresentados outros resultados obtidos para este modelo, tais como flutua\u00e7\u00f5es e grandes desvios.<\/p>\n<\/div>\n<\/div>\n

\u00a0<\/span><\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>13\/11
\nOperadores diferenciais generalizados e suas aplica\u00e7\u00f5es aos sistemas de part\u00edculas<\/em>
\nAlexandre Simas (UFPA)<\/span><\/a><\/h4><\/div>
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Neste semin\u00e1rio vamos come\u00e7ar definindo o operador diferencial generalizado que estamos interessados, definir brevemente os espa\u00e7os de W-Sobolev, e apresentar alguns resultados. Em seguida, vamos discutir a obten\u00e7\u00e3o de aproxima\u00e7\u00f5es deste operador por operadores definidos em discretiza\u00e7\u00f5es do dom\u00ednio. Finalmente mostraremos como definir sistemas de part\u00edculas induzidos por estes operadores e mostrar que esses sistemas satisfazem limites hidrodin\u00e2micos e flutua\u00e7\u00f5es no equil\u00edbrio. (Trabalho em conjunto com F\u00e1bio J. Valentim)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>02\/10
\nLayering transitions for the Solid-on-Solid model<\/em>
\nHubert Lacoin (IMPA)<\/span><\/a><\/h4><\/div>
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\nA ser definido
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<\/i><\/i><\/span>18\/09
\nCompetition in growth and urns<\/em>
\nSimon Griffiths (PUC-Rio)<\/span><\/a><\/h4><\/div>
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We consider an urn model with graph based interactions and ask the question: when can two competing growths (in different colors) co-exist? We discuss this problem in finite graphs and infinite lattices. We also discuss an application to co-existence of competing bootstrap type growth models Based on joint work with Daniel Ahlberg, Svante Janson and Robert Morris.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>21\/08
\nEntropia relativa e flutua\u00e7\u00f5es de sistemas de part\u00edculas<\/em>
\nOt\u00e1vio Menezes (IMPA)<\/span><\/a><\/h4><\/div>
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Nessa apresenta\u00e7\u00e3o, exporemos uma t\u00e9cnica para estimar a entropia relativa entre a lei de um sistema de part\u00edculas e uma lei produto. Nos dois modelos que estudamos (passeio aleat\u00f3rio sobre um processo de exclus\u00e3o e modelo de rea\u00e7\u00e3o-difus\u00e3o) as cotas obtidas s\u00e3o melhores do que as exigidas pelo m\u00e9todo de Yau para a prova de limites hidrodin\u00e2micos. Acreditamos que a t\u00e9cnica pode ser adaptada para outros modelos e que essas estimativas de entropia podem ajudar no estudo das flutua\u00e7\u00f5es ao redor do limite hidrodin\u00e2mico de sistemas fora do equil\u00edbrio.
\nEste \u00e9 um trabalho em colabora\u00e7\u00e3o com Milton Jara.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>27\/06
\nGlobal survival of tree-like branching random walks<\/em>
\nCristian Coletti (UFABC)<\/span><\/a><\/h4><\/div>
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The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $lambda$. There is a threshold for $lambda$, which is called $lambda_w$, that separates almost sure global extinction from global survival. Only for some classes of branching random walks it is known that the global critical parameter $lambda_w$ is the inverse of a certain function of the reproduction rates, which we denote by $K_w$. We provide here new sufficient conditions which guarantee that the global critical parameter of tree-like branching random walks equals $1\/K_w$.<\/div>\n
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This result is part of a joint work with Bertacchi, D. and Zucca, F. (ALEA, v. 14, p. 381-402, 2017).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>05\/06
\nKalikow\u2019s condition reloaded: Renormalization methods for random walks in a non-i.i.d. random environment<\/em>
\nEnrique Guerra Aguilar (UFRJ)<\/span><\/a><\/h4><\/div>
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In spite of its simplicity, asymptotic behaviours of RWRE are not <\/span><\/a>well-understood, especially when the underlying dimension of the walk is bigger than 1. Significant progress has been done in the higher dimensional case and when the environment is i.i.d. by Alain-Sol Sznitman through a sequel of articles (c.f. [Sz01]- [Sz02]- [Sz03]). In a posterior work [BDR14] the authors were able to improve the aforementioned results by means of improving in turn the renormalization methods introduced by Sznitman. It is our purpose to extend the methods developed in these articles for environments which are non i.i.d. It is important to point out that non-i.i.d. random environments have been studied in [RA03] and [CZ01] among others, however by different reasons they do not make use of renormalization. As a very preliminary step, we would like to extend the ideas introduced in [Sz01]. Thus in this talk, we will see first an introduction of the model and introduce Kalikow\u2019s condition. Then we will explain the renewal structure in both: i.i.d. random environment and mixing environment. Finally we would like to contrast statements of some results for the two frameworks. This is work in progress.<\/div>\n
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References:[BDR14] N. Berger, A. Drewitz and A.F Ram\u00edrez. Effective Polynomial Ballisticity Conditions for Random Walk in Random Environment. Comm. Pure. Appl. Math. (2014).[CZ01] F. Comets and O. Zeitouni. A law of large numbers for random walks in random mixing environments. Ann. Probab. 32 , no. 1B, 88017914, (2004).[RA03] F. Rassoul-Agha. The point of view of the particle on the law of large numbers for random walks in a mixing random environment. Ann. Probab. 31 , no.
\n3, 1441171463, (2003).[Sz01] A.S. Sznitman. Slowdown estimates and central limit theorem for random walks in random environment.J. Eur. Math. Soc. 2, no. 2, 9317143 (2000).[Sz02] A.S. Sznitman. On a class of transient random walks in random environment. Ann. Probab. 29 (2), 724-765 (2001).[Sz03] A.S. Sznitman. An effective criterion for ballistic behavior of random walks in random environment. Probab. Theory Related Fields 122, no. 4, 509-544
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<\/i><\/i><\/span>22\/05
\nTransi\u00e7\u00e3o de fase para o modelo de percola\u00e7\u00e3o booleana no plano<\/em>
\nAugusto Q. Texeira (IMPA)<\/span><\/a><\/h4><\/div>
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Nesse semin\u00e1rio, falaremos sobre um tipo de percola\u00e7\u00e3o dependente chamada: percola\u00e7\u00e3o booleana. Come\u00e7amos com um processo de pontos de Poisson em R^2 com densidade u e colocamos bolas de raios aleat\u00f3rios centradas em cada um desses pontos. Nesse modelo, sob condi\u00e7\u00f5es bastante gerais sobre as caudas dos raios, sabemos que existe um u_c > 0 tal que: \u2013 se u < u_c, temos que o conjunto vacante (n\u00e3o tocado pelas bolas) possui uma \u00fanica componente conexa ilimitada enquanto o conjunto ocupado (composto pela uni\u00e3o das bolas) possui somente componentes limitadas. – se u = u_c, nem o conjunto vacante nem o conjunto ocupado possuem componentes ilimitadas. – se u > u_c, temos uma \u00fanica componente ilimitada no conjunto ocupado e o tamanho de uma componente vacante t\u00edpica possui caudas exponenciais. As t\u00e9cnicas das quais falaremos nesse semin\u00e1rio se aplicam a outros modelos de percola\u00e7\u00e3o tais como Voronoi e confetti. Esse semin\u00e1rio \u00e9 fruto de uma colabora\u00e7\u00e3o com Daniel Ahlberg e Vincent Tassion.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>08\/05A version of the random directed forest and its convergence to the Brownian web<\/em>
\nLeonel Zuazn\u00e1bar (IM-UFRJ)<\/span><\/a><\/h4><\/div>
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Several authors have studied convergence in distribution to the Brownian web <\/span><\/a>under diffusive scaling of Markovian random walks. In a paper by R. Roy, K. Saha and A. Sarkar, convergence to the Brownian web is proved for a system of coalescing random paths \u2013 the Random Directed Forest- which are not Markovian. Paths in the Random Directed Forest do not cross each other before coalescence. Here we study a generalization of the non-Markovian Random Directed Forest where paths can cross each other and prove convergence to the Brownian web. This provides an example of how the techniques to prove convergence to the Brownian web for systems allowing crossings can be applied to non-Markovian systems.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>17\/04
\nTruncated long-range percolation on oriented graphs<\/em>
\nBernardo Nunes (UFMG)<\/span><\/a><\/h4><\/div>
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We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process. Joint work with Aernout van Enter and Daniel Valesin.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>10\/04
\nGrowing Networks with Random Walks<\/em>
\nGiulio Iacobelli (PESC\/COPPE- UFRJ)<\/span><\/a><\/h4><\/div>
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Network growth and evolution is a fundamental theme that has puzzled scientists for the past decades. A number of models have been proposed to capture important properties of real networks, the most famous being the model of Barab\u00e1si-Albert (BA) which embodies the principle of preferential attachment. A recognized drawback of most proposed network growth models is the assumption of global information about the network. For example, the BA model requires the knowledge of the degree of every node in the network to randomly choose where a new node will be connected.<\/div>\n
In this work we propose and study a network growth model that is purely local. The model is based on a continuously moving random walk that after s steps connects a new node to its current location. Through extensive simulations and theoretical arguments, we analyze the behavior of the model finding a fundamental dependency on the parity of s, where networks with either exponential or heavy-tailed degree distribution can emerge. As s increases, parity dependency diminishes and the model recovers the degree distribution of BA preferential attachment model. The proposed purely local model indicates that networks can grow to exhibit interesting properties even in the absence of any global information.<\/div>\n
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Joint work with Bernardo Amorim, Daniel Figueiredo, and Giovanni Neglia.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>03\/04
\nFlutua\u00e7\u00f5es no equil\u00edbrio para uma modelo discreto do tipo Atlas<\/em>
\nFreddy Hernandez (IME-UFF)<\/span><\/a><\/h4><\/div>
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Consideramos uma vers\u00e3o discreta do chamado \"Atlas model\", que corresponde a uma sequ\u00eancia de processos de alcance zero (zero-range) numa linha semi-infinita, com uma fonte na origem e uma densidade de part\u00edculas divergente. Mostramos que as flutua\u00e7\u00f5es no equil\u00edbrio do modelo s\u00e3o regidas por uma equa\u00e7\u00e3o do calor estoc\u00e1stica com condi\u00e7\u00f5es de contorno de Neumann. Como consequ\u00eancia, mostramos que a corrente de part\u00edculas na origem converge para um movimento Browniano fracion\u00e1rio com exponente de Hurst $H = frac$.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>

<\/i><\/i><\/span>03\/02
\nA stronger topology for the Brownian web<\/em>
\nLuiz Renato Fontes (IME-USP)<\/span><\/a><\/h4><\/div>
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We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the diffusively rescaled weight distribution in a silo model (as well as the related output distribution in a river basin model), interpreted in terms of (dual) diffusively rescaled coalescing random walks, to corresponding objects defined in terms of the Brownian web.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"100-width.php","meta":{"footnotes":""},"class_list":["post-299","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/pages\/299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/comments?post=299"}],"version-history":[{"count":5,"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/pages\/299\/revisions"}],"predecessor-version":[{"id":304,"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/pages\/299\/revisions\/304"}],"wp:attachment":[{"href":"https:\/\/ppge.im.ufrj.br\/en\/wp-json\/wp\/v2\/media?parent=299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}