56 citations · 363 across the 34 of their papers we have counts for
13 papers · 1 filter
Free Perpetuities I: Existence, Subordination and Tail Asymptotics
Serban Belinschi, Bartosz Kołodziejek, Kamil Szpojankowski
We study the free analogue of the classical affine fixed-point (or perpetuity) equation \[ \mathbb{X} \stackrel{d}{=} \mathbb{A}^{1/2}\mathbb{X}\,\mathbb{A}^{1/2} + \mathbb{B}, \]…
Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
Serban Belinschi, Mireille Capitaine, Sandrine Dallaporta +1
We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix an…
Large Deviation Principles via Spherical Integrals
Serban Belinschi, Alice Guionnet, Jiaoyang Huang
In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical…
Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices
Serban Belinschi, Charles Bordenave, Mireille Capitaine +1
We consider a square random matrix of size of the form where is a noncommutative polynomial, is a tuple of deterministic matrices converging in -distribu…
On the Global Fluctuations of Block Gaussian Matrices
Mario Diaz, James Mingo, Serban Belinschi
In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy…
Spectral properties of polynomials in independent Wigner and deterministic matrices
Serban Belinschi, Mireille Capitaine
On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interva…