q-Gaussian Processes: Non-commutative and Classical Aspects
Abstrak
Abstract: We examine, for −1<q<1, q-Gaussian processes, i.e. families of operators (non-commutative random variables) – where the at fulfill the q-commutation relations for some covariance function – equipped with the vacuum expectation state. We show that there is a q-analogue of the Gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q-Gaussian processes into corresponding (and much simpler) questions in the underlying Hilbert space. In particular, we use this idea to show that a large class of q-Gaussian processes possesses a non-commutative kind of Markov property, which ensures that there exist classical versions of these non-commutative processes. This answers an old question of Frisch and Bourret [FB].
Topik & Kata Kunci
Penulis (3)
M. Bożejko
Burkhard Kummerer
R. Speicher
Akses Cepat
- Tahun Terbit
- 1996
- Bahasa
- en
- Total Sitasi
- 379×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1007/s002200050084
- Akses
- Open Access ✓