# Tagged Questions

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1answer
94 views

### Finding the right σ-algebra. Question on uncertainty related to the secretary problem

Assume a number of iid. items is presented and the task was to stop under the objective of picking the best item. In this setting it is relevant what is the distribution of the values of the ...
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182 views

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### Existence of free operators, independent and with given distributions

Excuse me if the question is not appropriate for Mathoverflow. I havs asked it in math.stackexchange, but did not get any response. And so, I dared to put it here. I am trying to learn free ...
1answer
134 views

### Spacing of the largest singular values of Wishart matrix

Let $X \in \mathbb{R}^{n \times p}$ consist of iid $\mathcal{N}(0,1)$. Assume that $n/p$ converges to a positive constant. Denote by $\sigma_1 \ge \sigma_2 \ge \cdots \ge \sigma_{\min(n,p)} \ge 0$ the ...
0answers
73 views

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

In traditional (commutative) probability theory, sums of random variables correspond to convolutions of distribution functions, which plays well with the Fourier Transform. In free (noncommutative) ...
1answer
265 views

### Non-abelian freeness of SU_2

The distribution of the trace of a random element of $SU_2$ is the Sato-Tate distribution. The analogue of the Gaussian distribution in free probability theory is the Wigner semicircle distribution. ...
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279 views

1answer
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### Uniqueness of free complements

Let $A,B$ be subfactors of a II$_1$ factor $M$ with $A*B\simeq M$. That is, $A$ and $B$ are freely independent with respect to the trace and $M\simeq A\vee B$. We'll call $B$ a free complement for $A$ ...
3answers
540 views

### Relationship between free probability and deterministic graphs?

Consider the $N\times N$ matrix  M = \left(\begin{array} \\ 0 & 1 & & 0 \\ 1 & \ddots & \ddots & \\ & \ddots & \ddots & 1 \\ 0 & & 1 & 0 \\ \end{...
0answers
453 views

### Relationship between R-transform and free convolution of random matrices?

I've been using the R-transform to calculate the free convolution of the eigenvalue spectra of two random matrices and I am trying to understand how it works, and in particular how it relates to ...