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Given a chain complex with the only modification that each cell of thecomplex has a probability distribution assigned. We will call this complex - arandom complex and what should be understood in practice, is that we have aclassical chain complex whose cells appear and disappear according to someprobability distributions. In this paper, we will try to find the stochastichomology of random complex, whose simplices have independent discretedistributions.

Stochastic Homology. Reduction Formulas for Computing Stochastic Betti  Numbers of Maximal Random Complexes with Discrete Probabilities. Computation  and Applications