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References

  1. Belinschi, Serban Teodor. Complex analysis methods in noncommutative probability. Thesis (Ph.D.)–Indiana University. ProQuest LLC, Ann Arbor, MI, 2005. 102 pp. ISBN: 978-0542-23476-7 MR2707564
  2. Cowen, Carl C. Iteration and the solution of functional equations for functions analytic in the unit disk. Trans. Amer. Math. Soc. 265 (1981), no. 1, 69--95. MR0607108 (82i:30036)
  3. Ben Ghorbal, Anis; Schürmann, Michael. Non-commutative notions of stochastic independence. Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 3, 531--561. MR1919720 (2003k:46096)
  4. Hasebe, Takahiro. Monotone convolution and monotone infinite divisibility from complex analytic viewpoint. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 1, 111--131. MR2646794 (2011i:60036)
  5. Hasebe, Takahiro. Conditionally monotone independence I: Independence, additive convolutions and related convolutions. To appear in Infin. Dimens. Anal. Quantum Probab. Relat. Top. arXiv:0907.5473v4. Math. Review number not available.
  6. Hasebe, Takahiro; Saigo, Hayato. The monotone cumulants. To appear in Ann. Inst. Henri Poincaré Probab. Stat., arXiv:0907.4896v3. Math. Review number not available.
  7. Lehner, Franz. Cumulants in noncommutative probability theory. I. Noncommutative exchangeability systems. Math. Z. 248 (2004), no. 1, 67--100. MR2092722 (2005h:46091)
  8. Muraki, Naofumi. Monotonic convolution and monotonic Lévy-Hinčin formula, preprint, 2000. Math. Review number not available.
  9. Muraki, Naofumi. The five independences as quasi-universal products. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), no. 1, 113--134. MR1895232 (2003e:46113)
  10. Muraki, Naofumi. The five independences as natural products. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003), no. 3, 337--371. MR2016316 (2005h:46093)
  11. Nica, Alexandru; Speicher, Roland. Lectures on the combinatorics of free probability. London Mathematical Society Lecture Note Series, 335. Cambridge University Press, Cambridge, 2006. xvi+417 pp. ISBN: 978-0-521-85852-6; 0-521-85852-6 MR2266879 (2008k:46198)
  12. Rota, G.-C.; Taylor, B. D. The classical umbral calculus. SIAM J. Math. Anal. 25 (1994), no. 2, 694--711. MR1266584 (95d:05014)
  13. Saigo, Hayato. A simple proof for monotone CLT. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 2, 339--343. MR2669052 (2011i:46079)
  14. Speicher, Roland. Multiplicative functions on the lattice of noncrossing partitions and free convolution. Math. Ann. 298 (1994), no. 4, 611--628. MR1268597 (95h:05012)
  15. Speicher, Roland. On universal products. Free probability theory (Waterloo, ON, 1995), 257--266, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997. MR1426844 (98c:46141)
  16. Speicher, Roland; Woroudi, Reza. Boolean convolution. Free probability theory (Waterloo, ON, 1995), 267--279, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997. MR1426845 (98b:46084)
  17. Voiculescu, Dan. Symmetries of some reduced free product $C\sp \ast$-algebras. Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), 556--588, Lecture Notes in Math., 1132, Springer, Berlin, 1985. MR0799593 (87d:46075)
  18. Voiculescu, Dan. Addition of certain noncommuting random variables. J. Funct. Anal. 66 (1986), no. 3, 323--346. MR0839105 (87j:46122)
  19. Voiculescu, D. V.; Dykema, K. J.; Nica, A. Free random variables. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. CRM Monograph Series, 1. American Mathematical Society, Providence, RI, 1992. vi+70 pp. ISBN: 0-8218-6999-X MR1217253 (94c:46133)
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