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dohmatob
  • Member for 9 years, 6 months
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16 votes
3 answers
2k views

What is a good upper bound $n^n(n-1)^{n-1}\ldots2^21^1$?

13 votes
2 answers
796 views

Compute the integral $\int_0^1\int_0^1\ldots\int_0^1 f(x_1 + x_2 + \ldots + x_n)\,dx_1\,dx_2\ldots dx_n $

7 votes
1 answer
326 views

Negative moments of Marchenko-Pastur law

6 votes
1 answer
244 views

Is it true that if $\varepsilon > 0$ and $x \in int(A)$ then $\exists s > 0 \mid d(x,y) \ge \varepsilon + s,\;\forall y \not\in A^\varepsilon$?

5 votes
1 answer
488 views

When is a mapping the proximity operator of some convex function?

5 votes
2 answers
142 views

How to compute $\frac{1}{2\pi}\int_{-\pi}^\pi (\cos y + x)^{2k}dy$ and similar integrals

5 votes
2 answers
140 views

Sufficient condition for decreasing function $\phi:(0,\infty)\to (0,\infty)$ to obey $\int_x^\infty\phi(t)\mbox{d}t\le Cx\phi(x)$, with C = constant

5 votes
1 answer
93 views

Proximal operator of squared $\ell_1$-norm

4 votes
1 answer
128 views

Find all values of $c$ for which $(1+c)^k - c^k - kc^{k-1} \ge 0$

4 votes
3 answers
148 views

Analytic expression for $\mathbb E_X[(X^\top u)^p (X^\top v)^p]$, where $u$ and $v$ are fixed vectors in $\mathbb R^d$ and $X$ is uniform on sphere

4 votes
2 answers
134 views

General solution to a certain simple recurrence relation

4 votes
2 answers
363 views

I conjecture that there are infinitely many linear relations $p_n + p_{n + 3} = 2 p_{n + 2}$ in the sequence of primes!

4 votes
1 answer
155 views

Given that $m \le n!$, what's a good lower bound for $n$ as a function of $m$?

4 votes
1 answer
184 views

For what metric spaces $X$ do we have $(A^\varepsilon)^\varepsilon=A^{2\varepsilon}$ for every $A \subseteq X$?

4 votes
1 answer
377 views

Closed-form value for $\min_{x^T\Sigma x \le 1}\|x\|_1 - x^Ta$

4 votes
0 answers
230 views

Where is Axiom of Choice used in the proof of Riesz and/or Hahn-Banach extension theorems?

4 votes
1 answer
107 views

Function $T:X \rightarrow X$ with least Lipschitz constant, for which $\sup_{x \in X}d(T(x),x) \le r$.

4 votes
1 answer
44 views

Obtain upper bound on nonnegative non-increasing integrand $f(t)$ from bound of its integral $\int_{0}^\infty f(t)dt \le W$.

3 votes
3 answers
593 views

For large $n$, what is a good upper-bound for $\sqrt{1-x^{1/n}}$ valid for $x \in (0, 1)$?

3 votes
1 answer
156 views

On a certain discrepancy measure between probability distributions on the symmetric group of permutation $\mathfrak S_n$

3 votes
0 answers
40 views

Modern definition of unimodality for multivariate distributions and characterizations thereof

3 votes
1 answer
67 views

Let $\Phi$ be standard Gaussian CDF and $u > 0$. What is good u-bound for $\int_0^1\Phi(u/r - ur)dr$ as a function of $u$?

3 votes
0 answers
111 views

Rate of convergence of projection matrix

3 votes
1 answer
276 views

Remove cycles from digraph without losing information (aka howto 'dagify' a digraph)

3 votes
0 answers
73 views

Tail probability of sum of order statistics of distance from point to a set

3 votes
0 answers
74 views

A question on linear algebra (svd, etc.) and matrix optimization

3 votes
1 answer
188 views

Asymptotics of Bessel function of first kind

3 votes
0 answers
51 views

Approximate any Borel subset $A \subseteq R^n$ with a compact $B \subseteq A$ such that $\mu(A) - \mu(B)$ is arbitrarily small.

3 votes
2 answers
78 views

Closed-form formula for $E_{x}[\max(u^\top x,0)\max(v^\top x ,0)]$ where $u,v$ are fixed vectors in $\mathbb R^d$ and $x$ is uniform on the sphere

3 votes
1 answer
126 views

Analytic formula for integral $I_p(\theta) := \int_0^{2\pi}\cos(t)^p\cos(t-\theta)^pdt$

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