Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Dual Sudakov Minoration via Dimension Reduction - A Program   We propose a program for establishing a conjectural extension to the class of
(origin-symmetric) log-concave probability measures $\mu$, of the classical
dual Sudakov Minoration on the expectation of the supremum of a Gaussian
process: \begin{equation} \label{eq:abstract} M(Z_p(\mu), C \int ||x||_K d\mu
\cdot K) \leq \exp(C p) \;\;\, \forall p \geq 1 . \end{equation} Here $K$ is an
origin-symmetric convex body, $Z_p(\mu)$ is the $L_p$-centroid body associated
to $\mu$, $M(A,B)$ is the packing-number of $B$ in $A$, and $C > 0$ is a
universal constant. The Program consists of first establishing a Weak
Generalized Dual Sudakov Minoration, involving the dimension $n$ of the ambient
space, which is then self-improved to a dimension-free estimate after applying
a dimension-reduction step. The latter step may be thought of as a conjectural
"small-ball one-sided" variant of the Johnson--Lindenstrauss
dimension-reduction lemma. We establish the Weak Generalized Dual Sudakov
Minoration for a variety of log-concave probability measures and convex bodies
(for instance, this step is fully resolved assuming a positive answer to the
Slicing Problem). The Separation Dimension-Reduction step is fully established
for ellipsoids and, up to logarithmic factors in the dimension, for cubes,
resulting in a corresponding Generalized (regular) Dual Sudakov Minoration
estimate for these bodies and arbitrary log-concave measures, which are shown
to be (essentially) best-possible. Along the way, we establish a regular
version of (\ref{eq:abstract}) for all $p \geq n$ and provide a new direct
proof of Sudakov Minoration via The Program.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas