IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-07-19T15:03:11ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2012-02-22T16:18:26Z2014-12-05T09:31:58Zhttp://eprints.imtlucca.it/id/eprint/1151This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11512012-02-22T16:18:26ZPerturbative approach to the Bak-Sneppen modelWe study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of xc, the value of the avalanche exponent τ, and the asymptotic distribution of minimal fitnesses.Maddalena FeliciGuido Caldarelliguido.caldarelli@imtlucca.itAndrea GabrielliLuciano Pietronero2012-02-21T12:03:48Z2012-02-21T14:06:17Zhttp://eprints.imtlucca.it/id/eprint/1140This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11402012-02-21T12:03:48ZProbabilistic approach to the Bak-Sneppen modelWe study here the Bak-Sneppen model, a prototype model for the study of self-organized criticality. In this model several species interact and undergo extinction with a power-law distribution of activity bursts. Species are defined through their “fitness” whose distribution in the system is uniform above a certain threshold. Run time statistics is introduced for the analysis of the dynamics in order to explain the peculiar properties of the model. This approach based on conditional probability theory, takes into account the correlations due to memory effects. In this way, we may compute analytically the value of the fitness threshold with the desired precision. This represents a substantial improvement with respect to the traditional mean field approach.Guido Caldarelliguido.caldarelli@imtlucca.itMaddalena FeliciAndrea GabrielliLuciano Pietronero