Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spectral property for concurrent systems and some probabilistic
  applications   We study trace theoretic concurrent systems. This setting encompasses safe
(1-bounded) Petri nets. We introduce a notion of irreducible concurrent system
and we prove the equivalence between irreducibility and a "spectral property".
The spectral property states a strict inequality between radii of convergence
of certain growth series associated with the system. The proof that we present
relies on analytic combinatorics techniques. The spectral property is the
cornerstone of our theory, in a framework where the Perron-Frobenius theory
does not apply directly. This restriction is an inherent difficulty in the
study of concurrent systems.
  We apply the spectral property to the probabilistic theory of concurrent
systems. We prove on the one hand the uniqueness of the uniform measure, a
question left open in a previous paper. On the other hand, we prove that this
uniform measure can be realized as a Markov chain of states-and-cliques on a
state space that can be precisely characterized.

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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: q-fin