## References

SHOWING 1-10 OF 20 REFERENCES

### Convergence for noncommutative rational functions evaluated in random matrices

- Mathematics
- 2021

. One of the main applications of free probability is to show that for appropriately chosen independent copies of d random matrix models, any noncommutative polynomial in these d variables has a…

### Un critère de rationalité provenant de la géométrie non commutative

- Mathematics
- 1997

We prove a conjecture of A. Connes, which gives a rationality criterion for elements of the closure of ℂΓ (Γ a free group) in the space of bounded operators in l2(Γ). We show that this criterion…

### L 2-homology for von Neumann algebras

- Mathematics
- 2003

The aim of this paper is to introduce a notion of L-homology in the context of von Neumann algebras. Finding a suitable (co)homology theory for von Neumann algebras has been a dream for several…

### The free field: realization via unbounded operators and Atiyah property

- Mathematics
- 2019

Let $X_1,\dots,X_n$ be operators in a finite von Neumann algebra and consider their division closure in the affiliated unbounded operators. We address the question when this division closure is a…

### A Rationality Criterion for Unbounded Operators

- Mathematics
- 1999

Resume Let G be a group, let U ( G ) denote the set of unbounded operators on L 2 ( G ) which are affiliated to the group von Neumann algebra W ( G ) of G , and let D ( G ) denote the division…

### Noncommutative Rational Series with Applications

- Mathematics
- 2010

Preface Part I. Rational Series: 1. Rational series 2. Minimization 3. Series and languages 4. Rational expressions Part II. Arithmetic: 5. Automatic sequences and algebraic series 6. Rational series…

### q-Gaussian Processes: Non-commutative and Classical Aspects

- Mathematics
- 1997

Abstract: We examine, for −1<q<1, q-Gaussian processes, i.e. families of operators (non-commutative random variables) – where the at fulfill the q-commutation relations for some covariance…

### Lectures on the Combinatorics of Free Probability

- Mathematics
- 2006

Part I. Basic Concepts: 1. Non-commutative probability spaces and distributions 2. A case study of non-normal distribution 3. C*-probability spaces 4. Non-commutative joint distributions 5.…

### Free Ideal Rings and Localization in General Rings

- Mathematics
- 2006

Preface Note to the reader Terminology, notations and conventions used List of special notation 0. Preliminaries on modules 1. Principal ideal domains 2. Firs, semifirs and the weak algorithm 3.…

### Stochastic calculus with respect to free Brownian motion and analysis on Wigner space

- Mathematics
- 1998

Abstract. We define stochastic integrals with respect to free Brownian motion, and show that they satisfy Burkholder-Gundy type inequalities in operator norm. We prove also a version of Itô's…