| Abstract: |
| For a nonnegative density f and radially decreasing interaction potential W, the interaction energy is given by $E[f]= \int f(x)f(y)W(x-y) dxdy$. The celebrated Riesz rearrangement inequality says that $E[f] \le E[f^*]$, where $f^*$ is the radially decreasing rearrangement of $f$. In this talk, I will discuss the quantitative estimate of this inequality. I will first make an introduction about the problem and describe some previous results about the stability estimate for characteristic functions. I will then present a recent work with Yao Yao, where we establish the stability estimate for general densities. |
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