Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of minima of a random polynomial   We give an upper bound in O(d ^((n+1)/2)) for the number of critical points
of a normal random polynomial with degree d and at most n variables. Using the
large deviation principle for the spectral value of large random matrices we
obtain the bound
  O(exp(-beta n^2 + (n/2) log (d-1))) (beta is a positive constant independent
on n and d) for the number of minima of such a polynomial. This proves that
most normal random polynomials of fixed degree have only saddle points.
Finally, we give a closed form expression for the number of maxima (resp.
minima) of a random univariate polynomial, in terms of hypergeometric
functions.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
3
The categories of this paper are: physics
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs