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We study the outliers for two models which have an interesting connection. Onthe one hand, we study a specific class of planar Coulomb gases which aredeterminantal. It corresponds to the case where the confining potential is thelogarithmic potential of a radial probability measure. On the other hand, westudy the zeros of random polynomials that appear to be closely related to thefirst model. Their behavior far from the origin is shown to depend only on thedecaying properties of the probability measure generating the potential. Asimilar feature is observed for their behavior near the origin. Furthermore, insome cases, the appearance of outliers is observed, and the zeros of randompolynomials and the Coulomb gases are seen to exhibit exactly the samebehavior, which is related to the unweighted Bergman kernel.

Extremal particles of two-dimensional Coulomb gases and random polynomials on a positive background