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Free Probability.pdf

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Preview of Free Probability
🔗 Source: math.uni-sb.de
📊 Size: 214 KB
📄 Pages: 21 pages
⬇️ Downloads: 90

Summary

Free probability theory, originating in operator algebras, connects with random matrices, particularly in the limit N →∞ of N × N-random matrices, where moments converge. The theory provides concepts and notations for dealing with this limit without relying on random matrices. A combinatorial approach centers around free cumulants, which arise from the combinatorics of N × N-random matrices in the limit N = ∞ and are defined in terms of non-crossing partitions. The limit of random matrices is considered in terms of distribution, where moments of the matrices converge to moments of a variable, and this limit object lives in a 'non-classical probability space'. The concept of freeness appears when considering multiple variables, where joint moments are the surviving quantities, and variables are said to be free if they satisfy a certain condition with respect to a linear functional.

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Description

Free probability theory, originating in operator algebras, connects with random matrices, particularly in the limit N →∞ of N × N-random matrices, where...

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  • File Format: PDF
  • File Size: 214 KB
  • Pages: 21
  • Language: EN
  • Total Downloads: 90
  • Last Updated: 1 week ago

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