Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replica Symmetry in Upper Tails of Mean-Field Hypergraphs   Given a sequence of $s$-uniform hypergraphs $\{H_n\}_{n \geq 1}$, denote by
$T_p(H_n)$ the number of edges in the random induced hypergraph obtained by
including every vertex in $H_n$ independently with probability $p \in (0, 1)$.
Recent advances in the large deviations of low complexity non-linear functions
of independent Bernoulli variables can be used to show that tail probabilities
of $T_p(H_n)$ are precisely approximated by the so-called 'mean-field'
variational problem, under certain assumptions on the sequence $\{H_n\}_{n \geq
1}$. In this paper, we study properties of this variational problem for the
upper tail of $T_p(H_n)$, assuming that the mean-field approximation holds. In
particular, we show that the variational problem has a universal replica
symmetric phase (where it is uniquely minimized by a constant function), for
any sequence of regular $s$-uniform hypergraphs, which depends only on $s$. We
also analyze the associated variational problem for the related problem of
estimating subgraph frequencies in a converging sequence of dense graphs. Here,
the variational problems themselves have a limit which can be expressed in
terms of the limiting graphon.

35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin