Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Melonic dominance and the largest eigenvalue of a large random tensor   We consider a Gaussian rotationally invariant ensemble of random real totally
symmetric tensors with independent normally distributed entries, and estimate
the largest eigenvalue of a typical tensor in this ensemble by examining the
rate of growth of a random initial vector under successive applications of a
nonlinear map defined by the random tensor. In the limit of a large number of
dimensions, we observe that a simple form of melonic dominance holds, and the
quantity we study is effectively determined by a single Feynman diagram arising
from the Gaussian average over the tensor components. This computation suggests
that the largest tensor eigenvalue in our ensemble in the limit of a large
number of dimensions is proportional to the square root of the number of
dimensions, as it is for random real symmetric matrices.

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The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom