Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The limit of the smallest singular value of random matrices with i.i.d.
  entries   Let $\{a_{ij}\}$ $(1\le i,j<\infty)$ be i.i.d. real valued random variables
with zero mean and unit variance and let an integer sequence
$(N_m)_{m=1}^\infty$ satisfy $m/N_m\longrightarrow z$ for some $z\in(0,1)$. For
each $m\in{\mathbb N}$ denote by $A_m$ the $N_m\times m$ random matrix
$(a_{ij})$ $(1\le i\le N_m,1\le j\le m)$ and let $s_{m}(A_m)$ be its smallest
singular value. We prove that the sequence $\bigl({N_m}^{-1/2}
s_{m}(A_m)\bigr)_{m=1}^\infty$ converges to $1-\sqrt{z}$ almost surely. Our
result does not require boundedness of any moments of $a_{ij}$'s higher than
the $2$-nd and resolves a long standing question regarding the weakest moment
assumptions on the distribution of the entries sufficient for the convergence
to hold.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph