Timeline for Given a large random matrix, how to prove that every large submatrix whose range contains a large ball?

11 events

when toggle format	what		by	license	comment
Aug 6, 2020 at 10:10	comment	added	dohmatob		Could you make this claim more formal ?
Jul 25, 2020 at 1:42	comment	added	Rivers McForge		I mean, if we're talking probabilistically, there is a nonzero probability of arbitrarily big balls being in the range. Maybe it's unlikely, but asymptotically you could fit some truly ginormous balls in there.
Jul 24, 2020 at 19:43	history	edited	dohmatob	CC BY-SA 4.0	added 284 characters in body
Jul 24, 2020 at 19:17	history	edited	dohmatob	CC BY-SA 4.0	deleted 9 characters in body
Jul 24, 2020 at 19:06	history	edited	dohmatob	CC BY-SA 4.0	added 427 characters in body
Jul 24, 2020 at 17:51	history	edited	dohmatob	CC BY-SA 4.0	added 8 characters in body
Jul 24, 2020 at 16:03	comment	added	dohmatob		Indeed. Fixed. You may assume $m \le \delta n$ with $\delta \in (0, 1)$. Thus in the question, the universal constants $c_1$ and $c_2$ only depend on $\delta$.
Jul 24, 2020 at 16:02	history	edited	dohmatob	CC BY-SA 4.0	added 93 characters in body
Jul 24, 2020 at 15:53	comment	added	Robert Israel		Is there no relation between $m$ and $n$ except that they are both large? If $n < k$, it's impossible to have $c_2 {\mathbb B}^k \subseteq Z \mathbb B^n$.
Jul 24, 2020 at 15:05	history	edited	dohmatob	CC BY-SA 4.0	added 39 characters in body
Jul 24, 2020 at 15:00	history	asked	dohmatob	CC BY-SA 4.0