Width deviation of convex polygons

Shigeki Akiyama, Teturo Kamae

We consider the width $X_T(\omega )$ of a convex $n$-gon $T$ in the plane along the random direction $\omega \in \mathbb{R}/2\pi \mathbb{Z}$ and study its deviation rate: $$ δ(X_T)=\frac{\sqrt{\ma…