Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random concave functions on an equilateral lattice with periodic
  Hessians I: entropy and Laplacians   We show that a random concave function having a periodic hessian on an
equilateral lattice has a quadratic scaling limit, if the average hessian of
the function satisfies certain conditions. We consider the set of all concave
functions $g$ on an equilateral lattice $\mathbb L$ that when shifted by an
element of $n \mathbb L$, incur addition by a linear function (this condition
is equivalent to the periodicity of the hessian of $g$). We identify this set,
up to addition by a constant, with a convex polytope $P_n(s)$, where $s$
corresponds to the average hessian. We show that the $\ell_\infty$ diameter of
$P_n(s)$ is bounded below by $c(s) n^2$, where $c(s)$ is a positive constant
depending only on $s$. Our main result is that, for any $\epsilon_0 > 0$, the
normalized Lebesgue measure of all points in $P_n(s)$ that are not contained in
a $n^2$ dimensional cube $Q$ of sidelength $2 \epsilon_0 n^2$, centered at the
unique (up to addition of a linear term) quadratic polynomial with hessian $s$,
tends to $0$ as $n$ tends to $\infty$.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an