# Distances between zeroes and critical points for random polynomials with i.i.d. zeroes

@article{Kabluchko2018DistancesBZ, title={Distances between zeroes and critical points for random polynomials with i.i.d. zeroes}, author={Zakhar Kabluchko and Hauke Seidel}, journal={Electronic Journal of Probability}, year={2018}, volume={24} }

Consider a random polynomial $Q_n$ of degree $n+1$ whose zeroes are i.i.d. random variables $\xi_0,\xi_1,\ldots,\xi_n$ in the complex plane. We study the pairing between the zeroes of $Q_n$ and its critical points, i.e. the zeroes of its derivative $Q_n'$. In the asymptotic regime when $n\to\infty$, with high probability there is a critical point of $Q_n$ which is very close to $\xi_0$. We localize the position of this critical point by proving that the difference between $\xi_0$ and the… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

## On the local pairing behavior of critical points and roots of random polynomials

VIEW 5 EXCERPTS

CITES BACKGROUND, RESULTS & METHODS

HIGHLY INFLUENCED

## A Semicircle Law for Derivatives of Random Polynomials

VIEW 2 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 21 REFERENCES

## Pairing of Zeros and Critical Points for Random Polynomials

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Correlations and Pairing between Zeros and Critical Points of Gaussian Random Polynomials

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Pairing of zeros and critical points for random meromorphic functions on Riemann surfaces

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Esseen. Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Zeros of random polynomials and its higher derivatives

VIEW 1 EXCERPT