A short walk in quantum probability
2018 ◽
Vol 376
(2118)
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pp. 20170226
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Keyword(s):
This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue ‘Hilbert’s sixth problem’.
2012 ◽
Vol 41
(4)
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pp. 451-458
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Keyword(s):
Keyword(s):
2005 ◽
Vol 18
(3)
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pp. 665-685
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1999 ◽
Vol 36
(4)
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pp. 1218-1224
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1999 ◽
Vol 36
(04)
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pp. 1218-1224
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2002 ◽
Vol 39
(04)
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pp. 829-838
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2004 ◽
Vol 131
(3)
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pp. 459-478
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Keyword(s):
1992 ◽
Vol 24
(3)
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pp. 211-220
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2015 ◽
Vol 52
(3)
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pp. 786-796
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1985 ◽
Vol 21
(1)
◽
pp. 133-145
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