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Results tagged with convex-geometry
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user 121486
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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Reference request: books on convex analysis / geometry
I am interested in convex geometry and analysis, especially in its connections with high dimensional probability theory.
I was reading the book by Pisier, The volume of convex bodies and Banach space …
- 380
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vote
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answers
25
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Metric entropy of an ellipsoid
Let $B^d_2$ denote the unit ball of $\ell_2^d$ and let $T$ be an invertible linear map.
Consider the function
$$
H(T) := \log M(TB_2^d, B_2^d),
$$
which is the packing entropy for $TB_2^d$ by $B_2^d$ …
- 380
0
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Support function of the intersection of two $\ell_p$ balls
Denote $\|\cdot \|_p$ for the norm in $\ell_p^n$, where $1 \leq p \leq \infty$, and $n \geq 1$.
Let $(x^\star_i)$ denote a nonincreasing arrangement of the sequence $(|x_i|) \in \mathbb{R}^n$.
We defi …
- 380
0
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Projection of a gaussian random vector onto a convex body
Let $K \subset \mathbb{R}^n$ denote a convex body. Let $\Pi_K$ denote the projection onto $K$,
$$
\Pi_K(y) = \mathrm{arg\,min}_{x \in K} \|y - x\|,
$$
where $\|\cdot\|$ denotes the usual Euclidean no …
- 380