Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a quantitative reversal of Alexandrov's inequality   Alexandrov's inequalities imply that for any convex body $A$, the sequence of
intrinsic volumes $V_1(A),\ldots,V_n(A)$ is non-increasing (when suitably
normalized). Milman's random version of Dvoretzky's theorem shows that a large
initial segment of this sequence is essentially constant, up to a critical
parameter called the Dvoretzky number. We show that this near-constant behavior
actually extends further, up to a different parameter associated with $A$. This
yields a new quantitative reverse inequality that sits between the approximate
reverse Urysohn inequality, due to Figiel--Tomczak-Jaegermann and Pisier, and
the sharp reverse Urysohn inequality for zonoids, due to Hug--Schneider. In
fact, we study concentration properties of the volume radius and mean width of
random projections of $A$ and show how these lead naturally to such reversals.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom