A new approach to subordination results in free probability

By Serban Teodor Belinschi, Hari Bercovici. 2007

129 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f546d91daa84563d365c503a3f676e50b3be80ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The Lebesgue decomposition of the free additive convolution of two probability distributions (2006, unknown): “The computations above provide real numbers bµ, cµ, dµ, bν , cν , dν which depend polynomially on u, v, w, x, s, t so that hµ(z) = bµz + cµ z + dµ , hν(z) = bνz + cν z + dν , z ∈ C+.”
The arithmetic of distributions in free probability theory (2005, methodology): “Note that Bercovici and Belinschi [8] gave a related approach using other analytic methods.”
Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem (2013, methodology): “Before starting the proof, let us give a brief outline of the reasoning and the main difficulties we will encounter here compared to the scalar case proof from [4].”
Free Probability and Random Matrices (2014, background): “A particularly nice feature is that the subordination function can be recovered by ﬁxed point arguments, as shown in [7].”
Outliers in the spectrum of large deformed unitarily invariant models (2012, unknown): “(3) In particular (see [8]), for any z ∈ C ∪R so that ω1 is analytic at z, ω1(z) is the attracting fixed point of the self-map of C defined by w 7→ Fν(Fμ(w)− w + z)− (Fμ(w)− w).”
Edge universality for deformed Wigner matrices (2014, background): “11), the free convolution measure ω1 ⊞ ω2 can be described in terms of a set of functional equations for the Stieltjes transforms; see [10, 3].”
Extremal eigenvalues and eigenvectors of deformed Wigner matrices (2013, background): “2), the free convolution measure ω1 ⊞ ω2 can be described in terms of a set of functional equations for the Stieltjes transforms; see [39, 11, 5].”
Free Convolution with a Semicircular Distribution and Eigenvalues of Spiked Deformations of Wigner Matrices (2010, methodology): “Later, a new proof of this result was given in [10], using a fixed point theorem for analytic self-maps of the upper half-plane.”