Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernstein's inequality for general Markov chains   We establish Bernstein inequalities for functions of general
(general-state-space, not necessarily reversible) Markov chains. These
inequalities achieve sharp variance proxies and recover the classical
Bernstein's inequality under independence. The key analysis lies in upper
bounding the operator norm of a perturbed Markov transition kernel by the
limiting operator norm of a sequence of finite-rank and perturbed Markov
transition kernels. For each finite-rank and perturbed Markov kernel, we bound
its norm by the sum of two convex functions. One coincides with what delivers
the classical Bernstein's inequality, and the other reflects the influence of
the Markov dependence. A convex analysis on conjugates of these two functions
then derives our Bernstein inequalities.

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom