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Volumn 6, Issue 3, 2003, Pages 337-371

The five independences as natural products

Author keywords

Anti monotone product; Boolean product; Free product; Monotone product; Natural product; Noncommutative probability; Tensor product; Universal product

Indexed keywords


EID: 0348158588     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025703001365     Document Type: Article
Times cited : (115)

References (28)
  • 2
    • 0347976575 scopus 로고    scopus 로고
    • Non-commutative notions of stochastic independence
    • A. Ben Ghorbal and M. Schürmann, Non-commutative notions of stochastic independence, Math. Proc. Camb. Phil. Soc. 133 (2002) 531-561.
    • (2002) Math. Proc. Camb. Phil. Soc. , vol.133 , pp. 531-561
    • Ghorbal, A.B.1    Schürmann, M.2
  • 3
    • 0011912330 scopus 로고
    • Uniformly bounded representations of free groups
    • M. Bozejko, Uniformly bounded representations of free groups, J. Reine Angew. Math. 377 (1987) 170-186.
    • (1987) J. Reine Angew. Math. , vol.377 , pp. 170-186
    • Bozejko, M.1
  • 4
    • 0001072713 scopus 로고
    • A quantum mechanical central limit theorem
    • D. D. Cushen and R. L. Hudson, A quantum mechanical central limit theorem, J. Appl. Probab. 8 (1971) 454-469.
    • (1971) J. Appl. Probab. , vol.8 , pp. 454-469
    • Cushen, D.D.1    Hudson, R.L.2
  • 5
  • 6
    • 0010427894 scopus 로고    scopus 로고
    • Unification of boolean, monotone, anti-monotone, and tensor independence and Lévy processes
    • preprint, EMAU Greifswald
    • U. Franz, Unification of boolean, monotone, anti-monotone, and tensor independence and Lévy processes, preprint, EMAU Greifswald, 2001. To appear in Math. Z.
    • (2001) Math. Z.
    • Franz, U.1
  • 7
    • 0000739839 scopus 로고
    • An algebraic version of the central limit theorem
    • N. Giri and W. von Waldenfels, An algebraic version of the central limit theorem, Z. Wahr. Verw. Gebiete 42 (1978) 129-134.
    • (1978) Z. Wahr. Verw. Gebiete , vol.42 , pp. 129-134
    • Giri, N.1    Von Waldenfels, W.2
  • 8
    • 0005141929 scopus 로고    scopus 로고
    • The Semicircle Law, Free Random Variables and Entropy
    • Amer. Math. Soc.
    • F. Hiai and D. Petz, The Semicircle Law, Free Random Variables and Entropy, Mathematical Surveys and Monographs, Vol. 77 (Amer. Math. Soc., 2000).
    • (2000) Mathematical Surveys and Monographs , vol.77
    • Hiai, F.1    Petz, D.2
  • 9
    • 0000938937 scopus 로고
    • A quantum mechanical central limit theorem for anticommuting observables
    • R. L. Hudson, A quantum mechanical central limit theorem for anticommuting observables, J. Appl. Probab. 10 (1973) 502-509.
    • (1973) J. Appl. Probab. , vol.10 , pp. 502-509
    • Hudson, R.L.1
  • 10
    • 0001753230 scopus 로고    scopus 로고
    • An interacting free Fock space and the arcsine law
    • Y. G. Lu, An interacting free Fock space and the arcsine law, Probab. Math. Statist. 17 (1997) 149-166.
    • (1997) Probab. Math. Statist. , vol.17 , pp. 149-166
    • Lu, Y.G.1
  • 11
    • 0003359771 scopus 로고
    • Quantum Probability for Probabilists
    • Springer
    • P. A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math. Vol. 1538 (Springer, 1993).
    • (1993) Lecture Notes in Math. , vol.1538
    • Meyer, P.A.1
  • 12
    • 0009946112 scopus 로고
    • A new example of noncommutative "de Moivre-Laplace theorem", in Probability Theory and Mathematical Statistics
    • Tokyo eds. S. Watanabe, M. Fukushima, Yu. V. Prohorov and A. N. Shiryaev World Scientific
    • N. Muraki, A new example of noncommutative "de Moivre-Laplace theorem", in Probability Theory and Mathematical Statistics, Proc. Seventh Japan-Russia Symp., Tokyo 1995, eds. S. Watanabe, M. Fukushima, Yu. V. Prohorov and A. N. Shiryaev (World Scientific, 1996), pp. 353-362.
    • (1995) Proc. Seventh Japan-Russia Symp. , pp. 353-362
    • Muraki, N.1
  • 13
    • 0031066534 scopus 로고    scopus 로고
    • Noncommutative Brownian motion in monotone Fock space
    • N. Muraki, Noncommutative Brownian motion in monotone Fock space, Commun. Math. Phys. 183 (1997) 557-570.
    • (1997) Commun. Math. Phys. , vol.183 , pp. 557-570
    • Muraki, N.1
  • 14
    • 0035589802 scopus 로고    scopus 로고
    • Monotonic independence, monotonic central limit theorem and monotonic law of small numbers
    • N. Muraki, Monotonic independence, monotonic central limit theorem and monotonic law of small numbers, Infinite Dim. Anal. Quantum Probab. 4 (2001) 39-58.
    • (2001) Infinite Dim. Anal. Quantum Probab. , vol.4 , pp. 39-58
    • Muraki, N.1
  • 15
    • 0346715809 scopus 로고    scopus 로고
    • Monotonic convolution and monotonic Lévy-Hinčin formula
    • preprint, Iwate Pref. Univ.
    • N. Muraki, Monotonic convolution and monotonic Lévy-Hinčin formula, preprint, Iwate Pref. Univ., 2000, submitted to Probab. Theory Rel. Fields.
    • (2000) Probab. Theory Rel. Fields
    • Muraki, N.1
  • 16
    • 0036012377 scopus 로고    scopus 로고
    • The five independences as quasi-universal products
    • N. Muraki, The five independences as quasi-universal products, Infinite Dim. Anal. Quantum Probab. 5 (2002) 113-134.
    • (2002) Infinite Dim. Anal. Quantum Probab. , vol.5 , pp. 113-134
    • Muraki, N.1
  • 18
    • 0003342920 scopus 로고
    • White Noise on Bialgebras
    • Springer
    • M. Schürmann, White Noise on Bialgebras, Lecture Notes in Math., Vol. 1544 (Springer, 1993).
    • (1993) Lecture Notes in Math. , vol.1544
    • Schürmann, M.1
  • 19
    • 0001810924 scopus 로고
    • Direct sums of tensor products and non-commutative independence
    • M. Schürmann, Direct sums of tensor products and non-commutative independence, J. Funct. Anal. 133 (1995) 1-9.
    • (1995) J. Funct. Anal. , vol.133 , pp. 1-9
    • Schürmann, M.1
  • 20
    • 0038142595 scopus 로고
    • Non-commutative probability on algebraic structures, in Probability Measures on Groups and Related Structures XI
    • ed. H. Heyer World Scientific
    • M. Schürmann, Non-commutative probability on algebraic structures, in Probability Measures on Groups and Related Structures XI, Proc., Oberwolfach 1994, ed. H. Heyer (World Scientific, 1995), pp. 332-356.
    • (1994) Proc., Oberwolfach , pp. 332-356
    • Schürmann, M.1
  • 21
    • 0001709714 scopus 로고
    • A new example of "independence" and "white noise"
    • R. Speicher, A new example of "independence" and "white noise", Probab. Theorem Rel. Fields 84 (1990) 141-159.
    • (1990) Probab. Theorem Rel. Fields , vol.84 , pp. 141-159
    • Speicher, R.1
  • 22
    • 0009890105 scopus 로고
    • On universal products
    • Free Probability Theory, Proc., Toronto, Canada ed. D. V. Voiculescu, Amer. Math. Soc.
    • R. Speicher, On universal products, in Free Probability Theory, Proc., Toronto, Canada 1995, ed. D. V. Voiculescu, Fields Inst. Commun., Vol. 12 (Amer. Math. Soc., 1997), pp. 257-266.
    • (1995) Fields Inst. Commun. , vol.12 , pp. 257-266
    • Speicher, R.1
  • 23
    • 0000003118 scopus 로고
    • Boolean convolution
    • Free Probability Theory, Proc., Toronto, Canada ed. D. V. Voiculescu, Amer. Math. Soc.
    • R. Speicher and R. Woroudi, Boolean convolution, in Free Probability Theory, Proc., Toronto, Canada 1995, ed. D. V. Voiculescu, Fields Inst. Commun., Vol. 12 (Amer. Math. Soc., 1997), pp. 267-279.
    • (1995) Fields Inst. Commun. , vol.12 , pp. 267-279
    • Speicher, R.1    Woroudi, R.2
  • 25
    • 0001146474 scopus 로고
    • Symmetries of some reduced free product C* -algebras
    • Operator Algebras and their Connections with Topology and Ergodic Theory, Proc., Buşteni, Romania eds. H. Araki, C. C. Moore, Ş. Strǎtilǎ and D. V. Voiculescu, Springer
    • D. V. Voiculescu, Symmetries of some reduced free product C* -algebras, in Operator Algebras and their Connections with Topology and Ergodic Theory, Proc., Buşteni, Romania 1983, eds. H. Araki, C. C. Moore, Ş. Strǎtilǎ and D. V. Voiculescu, Lecture Notes in Math., Vol. 1132 (Springer, 1985), pp. 556-588.
    • (1983) Lecture Notes in Math. , vol.1132 , pp. 556-588
    • Voiculescu, D.V.1
  • 26
    • 0010172088 scopus 로고
    • Dual algebraic structures on operator algebras related to free products
    • D. V. Voiculescu, Dual algebraic structures on operator algebras related to free products, J. Operator Theory 17 (1987) 85-98.
    • (1987) J. Operator Theory , vol.17 , pp. 85-98
    • Voiculescu, D.V.1
  • 27
    • 0003047501 scopus 로고
    • An approach to the theory of pressure broadening of spectral lines
    • Probability and Information Theory II, eds. M. Behara, K. Krickeberg and J. Wolfowitz, Springer
    • W. von Waldenfels, An approach to the theory of pressure broadening of spectral lines, in Probability and Information Theory II, eds. M. Behara, K. Krickeberg and J. Wolfowitz, Lecture Notes in Math., Vol. 296 (Springer, 1973) pp. 19-69.
    • (1973) Lecture Notes in Math. , vol.296 , pp. 19-69
    • Von Waldenfels, W.1
  • 28
    • 0000739841 scopus 로고
    • An algebraic central limit theorem in the anticommuting case
    • W. von Waldenfels, An algebraic central limit theorem in the anticommuting case, Z. Wahr. Verw. Gebiete 42 (1978) 135-140.
    • (1978) Z. Wahr. Verw. Gebiete , vol.42 , pp. 135-140
    • Von Waldenfels, W.1


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