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The Oslo sandpile model, or if one wants to be precise, ricepile model, is acellular automaton designed to model experiments on granular piles displayingself-organized criticality. We present an analytic treatment that allows thecalculation of the transition probabilities between the differentconfigurations of the system; from here, using the theory of Markov chains, wecan obtain the stationary occupation distribution, which tell us that the phasespace is occupied with probabilities that vary in many orders of magnitude fromone state to another. Our results show how the complexity of this simple modelis built as the number of elements increases, and allows, for a given systemsize, the exact calculation of the avalanche size distribution and otherproperties related to the profile of the pile.Comment: many pages but not so many text, 5 figure

Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model