We provide a spectral norm concentration inequality for infinite random matrices with independent rows. This complements earlier results by Mendelson, Pajor, Oliveira and Rauhut. As an application we study L_2-norm sampling discretization and recovery of functions in RKHS on D \subset \mathbb{R \R ^d based on random function samples , where we only assume the finite trace of the kernel . We provide several concrete estimates with precise constants for the corresponding worst-case errors. The fail probability is controlled and decays polynomially in n, the number of samples. In general, our analysis does not need any additional assumptions and also includes the case of kernels on non-compact domains. However, under the mild additional assumption of separability we observe improved rates of convergence  .
In this paper we study L_2-norm sampling discretization and sampling recovery of complex-valued functions in RKHS on D \subset \R ^d based on random function samples . We only assume the finite trace of the kernel (Hilbert-Schmidt embedding into L_2) and provide several concrete estimates with precise constants for the corresponding worst-case errors. In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut .
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non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the
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related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut