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

Abstract

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