Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cut norm discontinuity of triangular truncation of graphons   The space of $L^p$ graphons, symmetric measurable functions $w: [0,1]^2 \to
\mathbb{R}$ with finite $p$-norm, features heavily in the study of sparse graph
limit theory. We show that the triangular cut operator $M_{\chi}$ acting on
this space is not continuous with respect to the cut norm. This is achieved by
showing that as $n\to \infty$, the norm of the triangular truncation operator
$\mathcal{T}_n$ on symmetric matrices equipped with the cut norm grows to
infinity as well. Due to the density of symmetric matrices in the space of
$L^p$ graphons, the norm growth of $\mathcal{T}_n$ generalizes to the
unboundedness of $M_{\chi}$. We also show that the norm of $\mathcal{T}_n$
grows to infinity on symmetric matrices equipped with the operator norm.

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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin