Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems
By Franz Lehner. 2002
78 citations recorded by the source corpus.
Abstract.Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting. It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the formula says that cumulants are moments of a certain ‘‘discrete Fourier transform’’ of a random variable. This provides a simple unified method to understand the known examples of cumulants, like classical, free and various q-cumulants.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e064f73019ad6e4d5b675c7d57abe463ec6ae8c2
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In Mathematical Physics
- Roland Speicher
- Piotr Śniady
- James A. Mingo
- Moritz Weber
- T. Banica
- Sven Raum
- Benoît Collins
- Alice Guionnet
In Statistics and Probability
- Roland Speicher
- Piotr Śniady
- James A. Mingo
- Benoît Collins
- Moritz Weber
- Alice Guionnet
- Sven Raum
- T. Banica
Citations in the corpus
- Second order freeness and fluctuations of random matrices: II. Unitary random matrices (2004, methodology): “blocks of C. We shall need the following formula for the second cumulant of the product of random variables, see for example [ L , 3.2].”