Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Overcrowding and hole probabilities for random zeros on complex
  manifolds   We give asymptotic large deviations estimates for the volume inside a domain
U of the zero set of a random polynomial of degree N, or more generally, of a
holomorphic section of the N-th power of a positive line bundle on a compact
Kaehler manifold. In particular, we show that for all $\delta>0$, the
probability that this volume differs by more than $\delta N$ from its average
value is less than $\exp(-C_{\delta,U}N^{m+1})$, for some constant
$C_{\delta,U}>0$. As a consequence, the "hole probability" that a random
section does not vanish in U has an upper bound of the form
$\exp(-C_{U}N^{m+1})$.

30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs