Lectures on the Combinatorics of Free Probability
By Alexandru Nica, Roland Speicher. 2006
1,171 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/4478c47208950c8897a65253d33977c0e1730619
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Roland Speicher
- Florent Benaych-Georges
- Sven Raum
- Moritz Weber
- Ramon van Handel
- Debashis Paul
- Friedrich Götze
- Charles Bordenave
Citations in the corpus
- Free Probability and Random Matrices (2014, background): “In 1994, I developped a combinatorial theory of freeness, based on free cumulants; many consequences of this approach were worked out together with Nica, see [28, 30].”
- Universality for Random Tensors (2011, background): “This is particularly transparent in the combinatorial formulation of free probability theory of [28,34].”
- Matrix concentration inequalities and free probability (2021, background): “1) that arises from Voiculescu’s theory of free probability [29, 44]: one may modify the model by replacing the scalar Gaussian coefficients gi by noncommuting random matrices or operators.”
- Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method (2015, unknown): “Let nowx = ua ∈ (A, φ) beR-diagonal [25].”
- Asymptotics of unitary and orthogonal matrix integrals (2006, background): “where π is the Kreweras complement (see [26]) and Cq the catalan number.”
- Classification results for easy quantum groups (2009, background): “= x+iy we have zz∗ = x2 +y2. Another interesting example, of key relevance in free probability, is the fact that the squeezed version of Voiculescu’s circular law is Wigner’s semicircle law. See e.g. [27]. Theorem 7.6. The asymptotic law of χt = P[tn] i=1uii with t ∈ (0,1] is as follows: (1) For O∗ ”
- Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees (2013, methodology): “This latter technique is inspired by ideas in Free Probability theory [15], [18], an area that originally grew out of operator algebras but which has a number of applications to asymptotic random matrix theory [1].”
- Generating random density matrices (2010, unknown): “[42] A.”
- HOPF MONOIDS IN THE CATEGORY OF SPECIES (2012, unknown): “For information on free cumulants, see [47].”