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Fei Cao's user avatar
Fei Cao's user avatar
Fei Cao
  • Member for 4 years, 9 months
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13 votes
1 answer
431 views

prove a challenging inequality or find a counterexample to it

7 votes
2 answers
312 views

Prove that $0\le\int_0^1\log(u){\rm d}x+\frac1{2\pi^2}\int_0^1\frac1{u^2}\left(\frac{{\rm d}u}{{\rm d}x}\right)^2{\rm d}x$

7 votes
0 answers
379 views

A possible error in Villani's monograph “Hypocoercivity”

7 votes
1 answer
420 views

Modified Energy Method for Transformed Fokker-Planck Equation (Tricky Integration by parts...)

7 votes
1 answer
506 views

A possible bug in a highly cited paper (Adam gradient descent)?

6 votes
5 answers
253 views

Show that $\frac{1}{n}\sum_{j=1}^\infty \left( 1 - (1-p_j)^n\right) \to 0$ as $n \to \infty$

6 votes
1 answer
205 views

Proper linearization of ODEs of the form $\dot{x}(t) + f(x(t)) + \sigma(t) = 0$?

6 votes
1 answer
220 views

Showing $\frac{f(a+2b)+f(a-2b)}{2f(a)}\leq\sqrt{1-\left(\frac{b}{a(1-a)}\right)^2}$ for $f(x)=\sqrt{x(1-x)}$ with some constraints

6 votes
1 answer
304 views

Possibility of bounding $\sum_{n=0}^N |a_n|$ from above by $\sup_{z\in (0,1)} |\sum_{1\leq n\leq N} (1+z+\ldots+z^{n-1}) a_n|$

5 votes
3 answers
363 views

A tough definite integral using contour integration

5 votes
2 answers
295 views

Geometric implication of the Sobolev embedding

4 votes
1 answer
137 views

Bounding Euclidean norm by slanted 1-norm

4 votes
1 answer
153 views

Parseval-Plancherel type identity for probability generating function

4 votes
1 answer
278 views

Poincare inequality for Poisson random variables

4 votes
1 answer
208 views

Optimal Poincare constant (with constraints)

4 votes
1 answer
205 views

exact meaning of uniform integrability for empirical distributions

4 votes
0 answers
99 views

Understanding the fast sweeping algorithm for Eikonal equations

3 votes
0 answers
113 views

Meaning of $K'[\cdot]$ when $K$ is an symmetric Onsager (matrix) operator

3 votes
1 answer
158 views

Non-uniqueness of a Dirichlet's problem

3 votes
1 answer
93 views

A basic question on martingales and filtrations

3 votes
1 answer
102 views

A discrete Poincare inequality

3 votes
1 answer
27 views

Show that $K(t) = \int_0^t \mathrm{e}^{-Cs} \, D \, \mathrm{e}^{-C^\intercal s} \,\mathrm{d} s$ satisfies a given equation involving $K(\infty)$

3 votes
0 answers
81 views

Generalized second derivative of a concave and piecewise $C^2$ function

3 votes
1 answer
987 views

Wasserstein distance between two empirical measures

3 votes
1 answer
25 views

Lipschitz continuity of $\sqrt{f}$ for $f(x) = \sup_{\alpha \in T} \sum_{i=1}^d \left(\sum_{j=1}^D \alpha_j x_{ij}\right)^2$

3 votes
0 answers
101 views

Deriving inequalities from other inequalities

3 votes
3 answers
152 views

Prove or Disprove: $\sum_{n\geq 0} (3p^2_n - p_n - 2p^3_n) \leq 0$ for any probability mass ${\bf p} = (p_0,p_1,\ldots)$

3 votes
0 answers
37 views

On the derivation of some asymptotic expressions involving combinatorics

2 votes
0 answers
204 views

Control $\int_0^\infty |\psi(x)|^2 dx$ by $\int_0^\infty \int_0^\infty K(x+y)\psi(x) \psi(y) dxdy$

2 votes
1 answer
325 views

Quantitative bound on Wasserstein distances by $L^p$ distances?