Asymptotic geometry

Asymptotic geometry, also known as asymptotic geometric analysis or high-dimensional geometry, is a field of mathematics that investigates the geometric properties of finite-dimensional objects, such as convex bodies and normed spaces, as the dimension tends to infinity. It is at the intersection of convex geometry and functional analysis.

The primary objects of study are typically finite-dimensional normed spaces, which can be represented as ${\displaystyle \mathbb {R} ^{n}}$ equipped with a norm ${\displaystyle \|\cdot \|}$, or equivalently, a unit ball ${\displaystyle K_{X}=\{x\in \mathbb {R} ^{n}:\|x\|\leq 1\}}$, which is a centrally symmetric, compact, convex set with a non-empty interior.