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Summary
"Stochastic convergence" formalizes the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle into a pattern. The pattern may for instance be
• Convergence in the classical sense to a fixed value, perhaps itself coming from a random event
• An increasing similarity of outcomes to what a purely deterministic function would produce
• An increasing preference towards a certain outcome
• An increasing "aversion" against straying far away from a certain outcome
• That the probability distribution describing the next outcome may grow increasingly similar to a certain distribution