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Published in:
2014 | OriginalPaper | Chapter
2. Independence
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Abstract
Measure theory is a linear theory that could not describe the dependence structure of events or random variables. We enter the realm of probability theory exactly at this point, where we define independence of events and random variables. Independence is a pivotal notion of probability theory, and the computation of dependencies is one of the theory’s major tasks. We close this chapter with the investigation of a random graph model (bond percolation on the integer lattice): using independent coin flips the individual bonds in the lattice are either kept or deleted. The question of interest is whether there is an infinite connected component or not.