User dohmatob

1 vote

Upper-bound for spectral norm of the covariance matrix of a certain Gaussian vector with correlated entries

answered Jul 8, 2022 at 8:45

1 vote

Tight upper-bounds for the Gaussian width of intersection of intersection of hyper-ellipsoid and unit-ball

answered Oct 20, 2022 at 11:26

1 vote

Prove / disprove: If $1 \le n < N$ and $A$ is an $N \times n$ matrix with iid from $\mathcal N(0,1)$, then $s_\min(A) \ge c\sqrt{N}$ w.p $1-2e^{-N}$

answered Sep 19, 2020 at 23:22

1 vote

Bounds for the extreme singular-values of random matrix with thresholded entries

answered Feb 23, 2021 at 3:31

1 vote

Limiting eigenvalue distribution of $YY^\top$ where $Y_{ij} = X_{ij} + a$ and $X$ has iid rows from an isotropic log-concave distribution

answered Mar 9, 2021 at 21:05

1 vote

Accepted

Simple non-asymptotic upper-bound for packing number of a hamming cube

answered Mar 22, 2021 at 12:50

1 vote

Almost independence of $x^\top a$ and $x^\top b$ for $x$ uniform on the sphere in $\mathbb R^d$ and $a,b \in \mathbb R^d$ with $a^\top b = 0$

answered Apr 14, 2021 at 17:27

1 vote

Use statistical physics ideas ("replica trick") to compute asymptotic value of $\inf_{\|w\| \le r} (1/n)\|Xw-y\|^2$ for random $X$ and $y$

answered Jun 2, 2021 at 23:16

1 vote

Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier information alone

answered Jun 25, 2021 at 14:55

1 vote

Accepted

Relationship between volume and area

answered Jun 17, 2020 at 18:46

1 vote

Anti-concentration of Gaussian quadratic form

answered Aug 16, 2020 at 7:54

1 vote

Accepted

How to sample a path between 2 states in a Markov chain

answered Aug 17, 2017 at 12:10

1 vote

Accepted

Non-asymptotic tail bounds for $D_{\text{Hellinger}}(P\|\hat{P}_N)$

answered Nov 25, 2018 at 20:12

1 vote

Practical bounds for the Wasserstein distance in 2 dimensions

answered Dec 5, 2018 at 0:10

1 vote

Accepted

Anti-concentration: upper bound for $P(\sup_{a \in \mathbb S_{n-1}}\sum_{i=1}^na_i^2Z_i^2 \ge \epsilon)$

answered Jan 7, 2019 at 1:42

1 vote

Use covering number to get uniform concentration from pointwise concentration

answered Feb 1, 2019 at 6:54

1 vote

Isoperimetry on $[0, 1]^n$ w.r.t $\ell_p$ distance, with $p \in [1,\infty]$

answered May 28, 2019 at 6:13

1 vote

Estimating the shift in the $\lambda_{\max}$ of a matrix under a diagonal perturbation

answered Aug 30, 2015 at 11:23

1 vote

Accepted

Upper bound for $\mathbb P(|f(A+XX^T)-f(A)| > \epsilon)$, where $A$ is a fixed pd matrix and $X$ has random iid entries

answered Jun 10, 2020 at 17:24

1 vote

Mathematics of doodling and the winding number

answered Jun 12, 2020 at 17:04

0 votes

Lower bound for sum of binomial coefficients?

answered Aug 31, 2020 at 12:24

0 votes

How to prove that a Brownian bridge $\mathbb{P}(M[0, 1/2]\geq s)\leq 2\mathbb{P}(B(1/2)\geq s/2)?$

answered Jun 13, 2020 at 11:20

0 votes

Sum of Square of the Eigenvalues of Wishart Matrix

answered Jun 29, 2021 at 12:31

0 votes

Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

answered Aug 12, 2021 at 11:12

0 votes

Concentration inequality for norm of solution to nonlinear least-squares problem

answered Jan 13, 2021 at 15:51

0 votes

Minimal conditions on random vector $X \in R^n$ to ensure that $\lim_{t\to 0^+}\sup_{\|w\|_p = 1}\sup_{u \in \mathbb R}\mathbb P(|X'w-u| \le t)=0$

answered Nov 4, 2022 at 7:40

0 votes

Minimax estimation rate of sparse vector $w_\star$, w.r.t to mixed norm $\|\hat w_n-w_\star\| := \|\hat w_n - w_\star\|_2 + \|\hat w_n-w_\star\|_q$

answered Aug 10, 2022 at 12:32

0 votes

Under what general conditions is the set $S := \left\{\int_{X}v(x)\pi(x)\,\mathrm{d}P(x) \mid \pi: X \to A\right\}$ closed?

answered Apr 29, 2022 at 13:27

0 votes

Under what general conditions is the set $S := \left\{\int_{X}v(x)\pi(x)\,\mathrm{d}P(x) \mid \pi: X \to A\right\}$ closed?

answered Apr 30, 2022 at 13:36

0 votes

Hölder continuity of Radon transform of smooth function

answered May 16, 2022 at 11:48

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70 Answers

Upper-bound for spectral norm of the covariance matrix of a certain Gaussian vector with correlated entries

Tight upper-bounds for the Gaussian width of intersection of intersection of hyper-ellipsoid and unit-ball

Prove / disprove: If $1 \le n < N$ and $A$ is an $N \times n$ matrix with iid from $\mathcal N(0,1)$, then $s_\min(A) \ge c\sqrt{N}$ w.p $1-2e^{-N}$

Bounds for the extreme singular-values of random matrix with thresholded entries

Limiting eigenvalue distribution of $YY^\top$ where $Y_{ij} = X_{ij} + a$ and $X$ has iid rows from an isotropic log-concave distribution

Simple non-asymptotic upper-bound for packing number of a hamming cube

Almost independence of $x^\top a$ and $x^\top b$ for $x$ uniform on the sphere in $\mathbb R^d$ and $a,b \in \mathbb R^d$ with $a^\top b = 0$

Use statistical physics ideas ("replica trick") to compute asymptotic value of $\inf_{\|w\| \le r} (1/n)\|Xw-y\|^2$ for random $X$ and $y$

Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier information alone

Relationship between volume and area

Anti-concentration of Gaussian quadratic form

How to sample a path between 2 states in a Markov chain

Non-asymptotic tail bounds for $D_{\text{Hellinger}}(P\|\hat{P}_N)$

Practical bounds for the Wasserstein distance in 2 dimensions

Anti-concentration: upper bound for $P(\sup_{a \in \mathbb S_{n-1}}\sum_{i=1}^na_i^2Z_i^2 \ge \epsilon)$

Use covering number to get uniform concentration from pointwise concentration

Isoperimetry on $[0, 1]^n$ w.r.t $\ell_p$ distance, with $p \in [1,\infty]$

Estimating the shift in the $\lambda_{\max}$ of a matrix under a diagonal perturbation

Upper bound for $\mathbb P(|f(A+XX^T)-f(A)| > \epsilon)$, where $A$ is a fixed pd matrix and $X$ has random iid entries

Mathematics of doodling and the winding number

Lower bound for sum of binomial coefficients?

How to prove that a Brownian bridge $\mathbb{P}(M[0, 1/2]\geq s)\leq 2\mathbb{P}(B(1/2)\geq s/2)?$

Sum of Square of the Eigenvalues of Wishart Matrix

Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

Concentration inequality for norm of solution to nonlinear least-squares problem

Minimal conditions on random vector $X \in R^n$ to ensure that $\lim_{t\to 0^+}\sup_{\|w\|_p = 1}\sup_{u \in \mathbb R}\mathbb P(|X'w-u| \le t)=0$

Minimax estimation rate of sparse vector $w_\star$, w.r.t to mixed norm $\|\hat w_n-w_\star\| := \|\hat w_n - w_\star\|_2 + \|\hat w_n-w_\star\|_q$

Under what general conditions is the set $S := \left\{\int_{X}v(x)\pi(x)\,\mathrm{d}P(x) \mid \pi: X \to A\right\}$ closed?

Under what general conditions is the set $S := \left\{\int_{X}v(x)\pi(x)\,\mathrm{d}P(x) \mid \pi: X \to A\right\}$ closed?

Hölder continuity of Radon transform of smooth function