Open Access
November 2015 Some remarks on MCMC estimation of spectra of integral operators
Radosław Adamczak, Witold Bednorz
Bernoulli 21(4): 2073-2092 (November 2015). DOI: 10.3150/14-BEJ635


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. "Some remarks on MCMC estimation of spectra of integral operators." Bernoulli 21 (4) 2073 - 2092, November 2015.


Received: 1 November 2013; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1350.60027
MathSciNet: MR3378459
Digital Object Identifier: 10.3150/14-BEJ635

Keywords: approximation of spectra , kernel operators , MCMC algorithms , random matrices

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 4 • November 2015
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