We consider zeros of higher derivatives of various random polynomials and show that their
limiting empirical measures agree with those of roots of corresponding random polynomials …

Let $ p_n $ be a polynomial of degree $ n $ having all its roots on the real line distributed
according to a smooth function $ u (0, x) $. One could wonder how the distribution of roots …

We investigate the hydrodynamic behavior of zeroes of trigonometric polynomials under
repeated differentiation. We show that if the zeroes of a real-rooted, degree $ d …

Consider a random polynomial Pn of degree n whose roots are independent random
variables sampled according to some probability distribution μ 0 on the complex plane C. It …

The question about behavior of gaps between zeros of polynomials under differentiation is
classical and goes back to Marcel Riesz. Recently, Stefan Steinerberger formally derived a …

Let $ p_n:\mathbb {C}\rightarrow\mathbb {C} $ be a random complex polynomial whose
roots are sampled iid from a radial distribution $2\pi ru (r) dr $ in the complex plane. A …

Let $ p_n $ be a random, degree $ n $ polynomial whose roots are chosen independently
according to the probability measure $\mu $ on the complex plane. For a deterministic point …

We extend the free convolution of Brown measures of $ R $-diagonal elements introduced
by K\"{o} sters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional …

Let μ be a compactly supported probability measure on the real line. Bercovici-Voiculescu
and Nica-Speicher proved the existence of a free convolution power μ⊞ k for any real k≥ 1 …

We start with a random polynomial $ P^{N} $ of degree $ N $ with independent coefficients
and consider a new polynomial $ P_ {t}^{N} $ obtained by repeated applications of a fraction …