Tópicos sobre o modelo Bak-Sneppen

Abstract

The Bak-Sneppen model is known to be a simple model, exhibiting self-organized criticality. In this master thesis we’ll study in detail some topics about the Bak-Sneppen modell that, in a certain sense, contributed to the understanding of stationary distribution of the model. We’ll study the following articles: Rigorous self-organised criticality in the modified Bak-Sneppen model [13], by Meester and Sarkar, Bounds for avalanche critical values of the Bak–Sneppen model [3], by Gillett, Meester and Nuyens and Maximal avalanches in the Bak-Sneppen model [4], by Gillett, Meester and van der Wal. In the article Rigorous self-organised criticality in the modified Bak-Sneppen model, the authors prove that a modified version of the Bak-Sneppen model obeys power law behaviour for avalanche duration and range using a coupling with a branching process. In the article Bounds for avalanche critical values of the Bak–Sneppen model, the authors get bounds for one of avalanche critical values of the Bak-Sneppen model (for transitive and locally finite graphs) through two couplings: to the lower bound, the authors use a branching proces and, to the upper bound, the authors use a independent site percolation model. Finally, in the article Maximal avalanches in the Bak-Sneppen model, the authors study the avalanche duration behaviour (in finite graphs) with random threshold, and they get surprising results to the expected avalanche duration.