## Extremal particles of two-dimensional Coulomb gases and random polynomials on a positive background. (arXiv:1811.12225v1 [math.PR])

We study the extremal particles of the two-dimensional Coulomb gas with confinement generated by a radially symmetric positive background in the determinantal case and the zeros of the corresponding random polynomials. We show that when the background is supported on the unit disk, the point process of the particles outside of the disk converges towards a universal point process, i.e. that does not depend on the background. This limiting point process may be seen as the determinantal point process governed by the Bergman kernel on the complement of the unit disk. It has an infinite number of particles and its maximum is a heavy tailed random variable. To prove this convergence we study the case where the confinement is generated by a positive background outside of the unit disk. For this model we show that the point process of the particles inside the disk converges towards the determinantal point process governed by the Bergman kernel on the unit disk. In the case where the background查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We study the extremal particles of the two-dimensional Coulomb gas with confinement generated by a radially symmetric positive background in the determinantal case and the zeros of the corresponding random polynomials. We show that when the background is supported on the unit disk, the point process of the particles outside of the disk converges towards a universal point process, i.e. that does not depend on the background. This limiting point process may be seen as the determinantal point process governed by the Bergman kernel on the complement of the unit disk. It has an infinite number of particles and its maximum is a heavy tailed random variable. To prove this convergence we study the case where the confinement is generated by a positive background outside of the unit disk. For this model we show that the point process of the particles inside the disk converges towards the determinantal point process governed by the Bergman kernel on the unit disk. In the case where the background