Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Ergodic Theorems   We present recent results about the asymptotic behavior of ergodic products
of isometries of a metric space X. If we assume that the displacement is
integrable, then either there is a sublinear diffusion or there is, for almost
every trajectory in X, a preferred direction at the boundary. We discuss the
precise statement when X is a proper metric space and compare it with classical
ergodic theorems. Applications are given to ergodic theorems for nonintegrable
functions, random walks on groups and Brownian motion on covering manifolds.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph