The existence and uniqueness of one minimization problem

SIAM Student Seminar
Friday, February 5, 2010 - 13:00
1 hour (actually 50 minutes)
Skiles 255
School of Mathematics, Georgia Tech
We are dealing with the following minimization problem: inf {I(\mu): \mu is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int (x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the class of f(x) will be discussed.