Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic properties of sum- and max-stable stationary random fields via
  null and positive group actions   We establish characterization results for the ergodicity of stationary
symmetric $\alpha$-stable (S$\alpha$S) and $\alpha$-Frechet random fields. We
show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803]
remains valid in the multiparameter setting, that is, a stationary S$\alpha$S
($0<\alpha<2$) random field is ergodic (or, equivalently, weakly mixing) if and
only if it is generated by a null group action. Similar results are also
established for max-stable random fields. The key ingredient is the adaption of
a characterization of positive/null recurrence of group actions by Takahashi
[Kodai Math. Sem. Rep. 23 (1971) 131-143], which is dimension-free and
different from the one used by Samorodnitsky.

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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th