6 papers
A bivariate approach to realrootedness of special polynomials
Aurelien Xavier Gribinski
In this paper, we exhibit new monotonicity properties of roots of families of orthogonal polynomials depending polynomially on a parameter (Laguerre and Gegenbauer).…
On majorization for polynomials sharing a common interlacer
Aurelien Gribinski
We give necessary and sufficient conditions for majorization of realrooted polynomials sharing a common interlacer by means of residues coming from fraction decomposition. We also…
A theory of singular values for finite free probability
Aurelien Gribinski
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transform…
Existence and polynomial time construction of biregular, bipartite Ramanujan graphs of all degrees
Aurelien Gribinski, Adam W. Marcus
We prove that there exist bipartite, biregular Ramanujan graphs of every degree and every number of vertices provided that the cardinalities of the two sets of the bipartition divi…
A notion of entropy on the roots of polynomials
Aurelien Gribinski
We introduce a canonical notion of entropy for polynomials analogue to that of random variables in probability. We prove that entropy increases smoothly with respect to finite free…
A rectangular additive convolution for polynomials
Aurelien Gribinski, Adam W. Marcus
We define the rectangular additive convolution of polynomials with nonnegative real roots as a generalization of the asymmetric additive convolution introduced by Marcus, Spielman…