AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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Let $K\subset\R^n$ be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequality relating the Gaussian mean of the support function to its mean under the uniform measure on $K$, obtained through a heat-flow argument....
Let $K\subset\R^n$ be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequality relating the Gaussian mean of the support function to its mean under the uniform measure on $K$, obtained through a heat-flow argument....
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