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Doctoral Thesis
DOI
10.11606/T.45.2013.tde-02092014-201127
Document
Author
Full name
Marcio Watanabe Alves de Souza
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Pimentel, Leandro Pinto Rodrigues (President)
Coletti, Cristian Favio
Fontes, Luiz Renato Goncalves
Machado, Fabio Prates
Popov, Serguei
Title in Portuguese
Flutuações do choque no processo de Hammersley
Keywords in Portuguese
Flutuações do choque
Percolação de última passagem
Processo de Hammersley
Processos multiclasses
Abstract in Portuguese
No presente trabalho provamos resultados sobre as flutuações dos fluxos de partículas e das partículas marcadas no processo de Hammersley multiclasse. Os métodos das demonstrações são robustos, formulados de modo a serem aplicados em outros processos, em particular se aplicam ao processo de exclusão totalmente assimétrico multiclasse (TASEP multiclasse) e à seu respectivo modelo de percolação de última passagem. Os principais teoremas obtidos são um teorema central do limite para o choque, seu coeficiente de difusão e uma fórmula exata para a variância do fluxo de partículas de classe N >1 para o processo em equilíbrio multiclasse.
Title in English
Shock fluctuations in Hammersley process
Keywords in English
Hammersley process
Last passage percolation
Multiclass process
Shock fluctuations
Abstract in English
We prove fluctuations results concerning fluxes of particles and tagged particles on multiclass Hammersley process. The methods used are robust and apply to other processes, in particular all the proofs can be adapted to the Multiclass totally asymmetric simple exclusion process (Multiclass TASEP) and its respective last passage percolation model. The main theorems obtained are a central limit theorem for the shock, its diffusion coefficient and an exact formula for the variance of the $N$-th class particle flux in a stationary version of the multiclass process when N > 1.
 
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Publishing Date
2014-09-03
 
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