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We study three convolutions of polynomials in the context of free probability theory.
Bemerkungen zu einem Satz von J H Grace über die Wurzeln algebraischer Gleichungen
G Szegö · 1922
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On the location of the roots of certain types of polynomials
JL Walsh · 1922
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Orthogonal polynomials
Gabor Szegö · 1939
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Geometry of polynomials
M. Marden · 1966
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A general Lee-Yang theorem for one-component and multicomponent ferromagnets
Elliott H. Lieb and Alan D. Sokal · 1981
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Eigenvalues and condition numbers of random matrices
Alan Edelman · 1988
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Determinants of sums
Marvin Marcus · 1990
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Free probability theory
Dan V Voiculescu · 1997
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Matrix models for beta ensembles
Ioana Dumitriu and Alan Edelman · 2002
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Analytic theory of polynomials
Q.I. Rahman and G. Schmeisser · 2002
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generatingfunctionology
Herbert S Wilf · 2005
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Lectures on the combinatorics of free probability
Alexandru Nica and Roland Speicher · 2006
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Polynomials with the half-plane property and matroid theory
Petter Brandén · 2007
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The Lee-Yang and Pólya-Schur programs. II. Theory of stable polynomials and applications
J. Borcea and P. Brändén · 2009
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Rectangular random matrices, related convolution
Florent Benaych-Georges · 2009
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An introduction to random matrices
Greg W Anderson, Alice Guionnet, and Ofer Zeitouni · 2010
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Matrix analysis
Interlacing families I: Bipartite Ramanujan graphs of all degrees
Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava · 2015
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Interlacing families II: Mixed characteristic polynomials and the Kadison–Singer problem
Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava · 2015
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Interlacing families iv: Bipartite ramanujan graphs of all sizes
Adam W Marcus, Daniel A Spielman, and Nikhil Srivastava · 2015
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Ramanujan graphs in polynomial time
Michael B Cohen · 2016
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Cumulants for finite free convolution
Octavio Arizmendi and Daniel Perales · 2018
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Crystallization of Random Matrix Orbits
Vadim Gorin and Adam W Marcus · 2018
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Roger A Horn and Charles R Johnson · 2012
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Polynomial convolutions and (finite) free probability
Adam W Marcus · 2015
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Finite free convolutions of polynomials
Adam Marcus, Daniel A Spielman, and Nikhil Srivastava · 2015
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Sur les racines de l’équation x n= 0
Th J Stieltjes
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Ramanujan coverings of graphs
Chris Hall, Doron Puder, and William F Sawin · 2018
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On the further structure of the finite free convolutions
Jonathan Leake and Nick Ryder · 2018
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Personal communication. To appear in Princeton PhD thesis., 2019
Benno Mirabelli · 2019
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