Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractal properties of typical convex functions   We study the singularity (multifractal) spectrum of continuous convex
functions defined on $[0,1]^{d}$. Let $E_f({h}) $ be the set of points at which
$f$ has a pointwise exponent equal to $h$. We first obtain general upper bounds
for the Hausdorff dimension of these sets $E_f(h)$, for all convex functions
$f$ and all $h\geq 0$. We prove that for typical/generic (in the sense of
Baire) continuous convex functions $f:[0,1]^{d}\to \mathbb{R} $, one has $\dim
E_f(h) =d-2+h$ for all $h\in[1,2],$ and in addition, we obtain that the set $
E_f({h} )$ is empty if $h\in (0,1)\cup (1,+\infty)$. Also, when $f$ is typical,
the boundary of $[0,1]^{d}$ belongs to $E_{f}({0})$.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
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The categories of this paper are: stat