The concept of randomness is easy to grasp on an intuitive level but challenging to characterize in rigorous mathematical terms. In "Algorithmic Randomness" (May 2019), Rod Downey and Denis R. Hirschfeldt present a comprehensive discussion of this issue, incorporating the distinct perspectives of "statisticians, coders, and gamblers."
Randomness is also a concern to "modelers" who depend on simulation models driven by random number generators or analytic models built using probabilistic assumptions. In such cases, the underlying mathematical model is often an ergodic stochastic process, and the issue is whether the output of the simulator's random number generator or the observed behavior of the real-world system being modeled is "random enough" to establish confidence in the model's predictions.
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