Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independence ratio and random eigenvectors in transitive graphs   A theorem of Hoffman gives an upper bound on the independence ratio of
regular graphs in terms of the minimum $\lambda_{\min}$ of the spectrum of the
adjacency matrix. To complement this result we use random eigenvectors to gain
lower bounds in the vertex-transitive case. For example, we prove that the
independence ratio of a $3$-regular transitive graph is at least
\[q=\frac{1}{2}-\frac{3}{4\pi}\arccos\biggl(\frac{1-\lambda
_{\min}}{4}\biggr).\] The same bound holds for infinite transitive graphs: we
construct factor of i.i.d. independent sets for which the probability that any
given vertex is in the set is at least $q-o(1)$. We also show that the set of
the distributions of factor of i.i.d. processes is not closed w.r.t. the weak
topology provided that the spectrum of the graph is uncountable.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci