Title: Local equilibrium in the Bak-Sneppen model,
Abstract: The Bak Sneppen (BS) model is a very simple model that exhibits all the
richness of self-organized criticality theory. At the thermodynamic limit, the
BS model converges to a situation where all particles have a fitness that is
uniformly distributed between a critical value $p_c$ and 1. The $p_c$ value is
unknown, as are the variables that influence and determine this value. Here, we
study the Bak Sneppen model in the case in which the lowest fitness particle
interacts with an arbitrary even number of $m$ nearest neighbors. We show that
$p_{c,m}$ verifies a simple local equilibrium relationship. Based on this
relationship, we can determine bounds for $p_{c,m}$.