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Doctoral Thesis
DOI
10.11606/T.45.2009.tde-23092009-180822
Document
Author
Full name
Rafael de Mattos Grisi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Ferrari, Pablo Augusto (President)
Marchetti, Domingos Humberto Urbano
Fontes, Luiz Renato Goncalves
Groisman, Pablo José
Oliveira, Roberto Imbuzeiro Moraes Felinto de
Title in Portuguese
Deformação harmônica da triangulação de Delaunay
Keywords in Portuguese
ladrilhamento de Voronoi
medidas de Palm
processo de Harness
processo de Poisson
processo pontual ergódico
teorema ergódico.
triangulação de Delaunay
Abstract in Portuguese
Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica.
Title in English
Harmonic deformation of the Delaunay triangulation
Keywords in English
Delaunay triangulation
ergodic point process
ergodic theorem.
harness process
Palm measures
Poisson process
Voronoi tessellation
Abstract in English
Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.
 
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tese.pdf (5.30 Mbytes)
Publishing Date
2009-11-19
 
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