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Probabilistic aspects of causal dynamical triangulations: percolation

Grant number: 10/05891-2
Support type:Research Grants - Visiting Researcher Grant - International
Duration: August 09, 2010 - September 08, 2010
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Anatoli Iambartsev
Grantee:Anatoli Iambartsev
Visiting researcher: Stefan Zohren
Visiting researcher institution: Universiteit Leiden, Netherlands
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil


Lorentzian Triangulations was introduced in quantum gravity as a tentative to define a Lorentz path integral for gravitation as a sum over triangulations. We plan to study percolation properties of such type infinite triangulations. The main aim of the project is to prove phase transition for bond-percolation in infinite Lorentzian triangulations, and in particular, to prove that the critical percolation probability is 1/2. We plan to apply ideas of Bellóbas e Riordan in context of percolation in Delaunay triangulations. This work is interesting not only for physics, where there is a little number of analytical results for models with coupled matter, but also it is interesting for probability where percolation problems traditionally have great importance. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
SISKO, VALENTIN; YAMBARTSEV, ANATOLY; ZOHREN, STEFAN. A note on weak convergence results for infinite causal triangulations. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 32, n. 3, p. 597-615, AUG 2018. Web of Science Citations: 0.
SISKO, V.; YAMBARTSEV, A.; ZOHREN, S. Growth of Uniform Infinite Causal Triangulations. Journal of Statistical Physics, v. 150, n. 2, p. 353-374, JAN 2013. Web of Science Citations: 4.

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