User Roland Speicher

13 votes

Why is free probability a generalization of probability theory?

answered Jul 25, 2017 at 14:37

12 votes

Why did Voiculescu develop free probability?

answered Aug 2, 2017 at 21:19

8 votes

Free probability with unbounded random variables?

answered Jul 28, 2017 at 9:51

7 votes

Video lectures of mathematics courses available online for free

answered Oct 30, 2018 at 22:14

6 votes

Accepted

Combinatorial formula to compute the moments of the product of two free random variables

answered Mar 22, 2021 at 8:43

6 votes

Is there a noncommutative Gaussian?

answered May 10, 2022 at 20:06

5 votes

Free probability: A unitary group heuristic for the relationship between additive free convolution and free compression

answered Sep 14, 2023 at 14:01

4 votes

What are applications of asymptotic freeness of random matrices?

answered Feb 17 at 13:06

4 votes

Joint moments like $\tau(XYXYXY)$ in terms of individual moments of free variables $X,Y$

answered Mar 2 at 11:25

4 votes

Accepted

Quick derivation of classical probability theory from von Neumann algebraic framework

answered Feb 23, 2021 at 8:00

4 votes

Semicircle law universality elsewhere

answered Jul 29, 2017 at 18:27

4 votes

Independence of two noncommutative observables

answered Aug 3, 2017 at 19:11

4 votes

Does free probability have anything to say about the eigenvalue correlations of random matrices?

answered May 6, 2018 at 21:05

4 votes

Accepted

Brown measure of left shift operator

answered Jul 25, 2017 at 20:02

4 votes

What is known about the distribution of eigenvectors of random matrices?

answered Jul 27, 2017 at 20:21

4 votes

Accepted

Relating the R-transform in free probability to noncommutative group representations

answered Jul 27, 2017 at 20:36

3 votes

Why a random variable is better described by its cumulants than by its characteristic function?

answered Jul 28, 2017 at 16:21

3 votes

Q-Gaussian processes and probability space

answered Aug 24, 2021 at 21:35

3 votes

Video lectures of mathematics courses available online for free

answered Nov 14, 2023 at 17:39

2 votes

Accepted

Free multiplicative convolution of two random matrices

answered Aug 24, 2021 at 8:52

2 votes

Random complex eigenvalues and averages of traces

answered Aug 14, 2018 at 22:09

1 vote

Spectral density of $D + XX^T$

answered Jan 1, 2019 at 12:07

1 vote

The problems of global asymptotic freeness

answered Feb 6, 2019 at 20:02

1 vote

Constructive definition of noncommutative rational functions (aka free skew fields)

answered Dec 26, 2020 at 22:14

1 vote

Are they the $N\times N$ random matrices with real or complex entries asymptotically free?

answered Jul 2, 2018 at 10:42

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25 Answers

Why is free probability a generalization of probability theory?

Why did Voiculescu develop free probability?

Free probability with unbounded random variables?

Video lectures of mathematics courses available online for free

Combinatorial formula to compute the moments of the product of two free random variables

Is there a noncommutative Gaussian?

Free probability: A unitary group heuristic for the relationship between additive free convolution and free compression

What are applications of asymptotic freeness of random matrices?

Joint moments like $\tau(XYXYXY)$ in terms of individual moments of free variables $X,Y$

Quick derivation of classical probability theory from von Neumann algebraic framework

Semicircle law universality elsewhere

Independence of two noncommutative observables

Does free probability have anything to say about the eigenvalue correlations of random matrices?

Brown measure of left shift operator

What is known about the distribution of eigenvectors of random matrices?

Relating the R-transform in free probability to noncommutative group representations

Why a random variable is better described by its cumulants than by its characteristic function?

Q-Gaussian processes and probability space

Video lectures of mathematics courses available online for free

Free multiplicative convolution of two random matrices

Random complex eigenvalues and averages of traces

Spectral density of $D + XX^T$

The problems of global asymptotic freeness

Constructive definition of noncommutative rational functions (aka free skew fields)

Are they the $N\times N$ random matrices with real or complex entries asymptotically free?