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Analysis and simulation of random walks and exclusion processes over graphs


The goal of this project is to investigate some mathematical and statistical properties of random walks and exclusion processes on graphs using analytical and numerical techniques. Specifically, we intend (i) to investigate the probability distribution function of the cover time of planar (e.g., the square and the hexagonal lattices) and random graphs, in particular of the Kleinberg graph and its variants, since very little is known about the probability distribution of this random variable, and (ii) to investigate the dynamics of the simple exclusion process in discrete time over graphs, which has connections with several topics in statistics (e.g., the analysis of contingency tables with fixed marginals) and the theory of computation (e.g., the computation of the permanent of a matrix, a #P-complete problem) with the objective of clarifying the time of convergence of the dynamics to the steady state. Besides addressing these scientific issues, we also hope to establish a line of research in "complex systems" at the interface between statistical mechanics, discrete mathematics and its applications to systems modeling and to attract undergraduate and graduate students and collaborators interested in these areas. (AU)

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Scientific publications (4)
(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)
MENDONCA, J. RICARDO G.,. Empirical scaling of the length of the longest increasing subsequences of random walks. Journal of Physics A-Mathematical and Theoretical, v. 50, n. 8, . (15/21580-0)
MENDONCA, J. R. G.. A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect. Journal of Physics A-Mathematical and Theoretical, v. 51, n. 14, . (15/21580-0)
MENDONCA, J. RICARDO G.; SIMOES, ROLF O.. Density classification performance and ergodicity of the Gacs-Kurdyumov-Levin cellular automaton model IV. Physical Review E, v. 98, n. 1, . (15/21580-0)

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