Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of relative Gibbs and relative equilibrium measures for
  actions of countable amenable groups   We formulate and prove a very general relative version of the
Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of
configuration spaces over a finite alphabet such that for every absolutely
summable relative interaction, every translation-invariant relative Gibbs
measure is a relative equilibrium measure and vice versa. Neither implication
is true without some assumption on the space of configurations. We note that
the usual finite type condition can be relaxed to a much more general class of
constraints. By "relative" we mean that both the interaction and the set of
allowed configurations are determined by a random environment. The result
includes many special cases that are well known. We give several applications
including (1) Gibbsian properties of measures that maximize pressure among all
those that project to a given measure via a topological factor map from one
symbolic system to another; (2) Gibbsian properties of equilibrium measures for
group shifts defined on arbitrary countable amenable groups; (3) A Gibbsian
characterization of equilibrium measures in terms of equilibrium condition on
lattice slices rather than on finite sets; (4) A relative extension of a
theorem of Meyerovitch, who proved a version of the Lanford--Ruelle theorem
which shows that every equilibrium measure on an arbitrary subshift satisfies a
Gibbsian property on interchangeable patterns.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org