Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces   Let $X$ be a standard Gaussian random variable. For any $p \in (1, \infty)$,
we prove the existence of a universal constant $C_{p}>0$ such that the
inequality $$(\mathbb{E} |h'(X)|^{p})^{1/p} \geq C_{p} \sqrt{d} (\mathbb{E}
|h(X)|^{p})^{1/p}$$ holds for all $d\geq 1$ and all polynomials $h : \mathbb{R}
\to \mathbb{C}$ whose spectrum is supported on frequencies at least $d$, that
is, $\mathbb{E} h(X) X^{k}=0$ for all $k=0,1, \ldots, d-1$. As an application
of this optimal estimate, we obtain an affirmative answer to the Gaussian
analogue of a question of Mendel and Naor (2014) concerning the growth of the
Ornstein-Uhlenbeck operator on tail spaces of the real line. We also show the
same bound for the gradient of analytic polynomials in an arbitrary dimension.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg