• Bernoulli
  • Volume 21, Number 4 (2015), 2073-2092.

Some remarks on MCMC estimation of spectra of integral operators

Radosław Adamczak and Witold Bednorz

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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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Bernoulli Volume 21, Number 4 (2015), 2073-2092.

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

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approximation of spectra kernel operators MCMC algorithms random matrices


Adamczak, Radosław; Bednorz, Witold. Some remarks on MCMC estimation of spectra of integral operators. Bernoulli 21 (2015), no. 4, 2073--2092. doi:10.3150/14-BEJ635.

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