Equilibrium measure and capacity for a region in complex plane.

Speaker : Kartick Adhikari

Date : 21st October, 2014 (Tuesday)

Time : 09:15 pm – 10:15 pm

Venue : Lecture Hall I, Department of Mathematics

Abstract: Let E\subset \mathbb{C} and \mu be a probability measure such that Supp(\mu)\subset E. Consider the total energy -\int \log|z-t|d\mu(z)d\mu(t) due to the measure \mu. We are interested to find the measure for which total energy is minimized and supported in E. We will address the existence and uniqueness of this measure (Equilibrium measure). We will discuss about capacity of a region in the complex plane. Finally we will introduce the notion of weighted equilibrium measure and weighted capacity for a region in the complex plane.

Area: Probability Theory


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