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arXiv · 1311.7566

Some remarks on MCMC estimation of spectra of integral operators

Radosław Adamczak·Witold Bednorz
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Abstract

We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov chain, which complements the results by V. Koltchinskii and E. Giné for i.i.d. sequences. In a special case of Mercer's kernels and geometrically ergodic chains, we also provide exponential inequalities, quantifying the speed of convergence.

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Radosław Adamczak, Witold Bednorz. 2015-09-18. Some remarks on MCMC estimation of spectra of integral operators. https://doi.org/10.3150/14-bej635

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