Skip to main content

All Questions

Filter by
Sorted by
Tagged with
1 vote
0 answers
45 views

Inequality Involving Concave Monotonic Function

Assume that $ f: \mathbb{R} \to \mathbb{R}_+ $ is a concave, non-decreasing and positive function. Let $\mathbb{X}$ be a finite set consisting of $ 0\leq x_1 \leq x_2 \leq x_3 \leq \ldots \leq x_n$. ...
Alireza Bakhtiari's user avatar
1 vote
1 answer
195 views

Reference request: Inequalities involving convex sets and Gaussian variables stated in a paper by Talagrand

I'm looking for references for two facts that are stated without proof in the paper: Talagrand, M., Are all sets of positive measure essentially convex?, Lindenstrauss, J. (ed.) et al., Geometric ...
Samuel Johnston's user avatar
2 votes
0 answers
164 views

Log Sobolev inequality for log concave perturbations of uniform measure

Suppose $\Omega$ is a convex bounded open set of $\mathbb{R}^n$ (I would be happy with just $\Omega$ as the $n$-dimensional cube). Let $\mu$ be the uniform measure on $\Omega$ and consider the ...
Matt Rosenzweig's user avatar
5 votes
0 answers
158 views

Log Sobolev inequality uniform in parameters

Fix a positive integer $N$. For $\theta \in [0,2\pi]$, set $\sigma_k(\theta) :=(\cos(k\theta),\sin(k\theta)) \in S^1$ for each integer $1\leq k\leq N$. Now for vectors $x_1,\ldots,x_N\in \mathbb{R}^2$,...
Matt Rosenzweig's user avatar
1 vote
1 answer
67 views

Lower-bound for $\mathbb E[e^{-b(v^\top X - c)^2}]$, when $X$ is log-concave in high-dimensions

Let $d$ be a large positive integer. Fix a unit-vector $v \in \mathbb R^d$, and scalars $b,c \in \mathbb R$ with $b > 0$. Let $X$ be a log-concave random vector in $\mathbb R^d$ normalized so that ...
dohmatob's user avatar
  • 6,853
1 vote
0 answers
93 views

Bounds on the spherical measure of sub-level sets of quadratic forms

I'm wondering if there are any bounds on the spherical measure of sets of the form $$ \mu_n\left(\{y\in S^{n-1} : \frac{y_1^2}{y_2^2} < \alpha\}\right) \leq f(\alpha) $$ where $\alpha$ is some ...
squattyroo's user avatar