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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
2
votes
Probability theory over noncommutative ring?
Section 2.5 of David Ellerman's "Counting distinctions: on the conceptual foundations
of Shannon’s information theory" overviews the history of the sum of probability squares formula known as Gini coe …
3
votes
1
answer
513
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Probability theory over noncommutative ring? [closed]
Observation: Entropy is a metric over some non commutative ring. Indeed, if we exponentiate the standard entropy definition
$\displaystyle H(X) = -\sum_{x \in \mathcal{X}} p(x) \ln p(x).$
we'll get …