Preprint
Gaussian processes in Non-commutative probability
ArXiv.org
Cornell University
08/10/2024
DOI: 10.48550/arxiv.2408.10254
Abstract
Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a systematic study of p.d. B(H)-valued kernels and the associated of H-valued Gaussian processes, together with their correlation and transfer operators. In our consideration of B(H)-valued kernels, we drop the p.d. assumption. We show that input-output models can be computed for systems of signed kernels taking the precise form of realizability via associated transfer block matrices (of operators analogous to the realization transforms in systems theory), i.e., represented via 2\times2 operator valued block matrices. In the context of B(H)-valued kernels we present new results on regression with H-valued Gaussian processes.
Details
- Title: Subtitle
- Gaussian processes in Non-commutative probability
- Creators
- Palle E. T JorgensenJames Tian
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2408.10254
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 08/10/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984697020402771
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