Free probability is a branch of mathematics that studies noncommutative random variables and their relationships, especially in the context of operator algebras and quantum mechanics. It was developed by mathematicians such as Dan Voiculescu in the 1990s and has connections to both probability theory and functional analysis. Here are some key concepts related to free probability: 1. **Free Random Variables**: In free probability, random variables are considered to be "free" in a specific algebraic sense.

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  1. Functional analysis
  2. Fields of mathematical analysis
  3. Mathematical analysis
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