The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Akhiezer N.I., Glazman I.M.: Theory of Linear Operators in Hilbert Space. Ungar, New York, (1963).
  • Anshelevich, Michael. Free martingale polynomials. J. Funct. Anal. 201 (2003), no. 1, 228--261. MR1986160
  • Anshelevich, Michael. Orthogonal polynomials with a resolvent-type generating function. Trans. Amer. Math. Soc. 360 (2008), no. 8, 4125--4143. MR2395166
  • Anshelevich, Michael. Bochner-Pearson-type characterization of the free Meixner class. Adv. in Appl. Math. 46 (2011), no. 1-4, 25--45. MR2794011
  • Anshelevich, Michael; Młotkowski, Wojciech. Semigroups of distributions with linear Jacobi parameters. J. Theoret. Probab. 25 (2012), no. 4, 1173--1206. MR2993018
  • Barndorff-Nielsen, Ole E.; Thorbjørnsen, Steen. Self-decomposability and Lévy processes in free probability. Bernoulli 8 (2002), no. 3, 323--366. MR1913111
  • Benaych-Georges, Florent. Taylor expansions of $R$-transforms: application to supports and moments. Indiana Univ. Math. J. 55 (2006), no. 2, 465--481. MR2225442
  • Biane, Philippe. Processes with free increments. Math. Z. 227 (1998), no. 1, 143--174. MR1605393
  • Bożejko, Marek; Bryc, Włodzimierz. On a class of free Lévy laws related to a regression problem. J. Funct. Anal. 236 (2006), no. 1, 59--77. MR2227129
  • Bożejko, Marek; Lytvynov, Eugene. Meixner class of non-commutative generalized stochastic processes with freely independent values. I. A characterization. Comm. Math. Phys. 292 (2009), no. 1, 99--129. MR2540072
  • Bożejko, Marek; Lytvynov, Eugene. Meixner class of non-commutative generalized stochastic processes with freely independent values II. The generating function. Comm. Math. Phys. 302 (2011), no. 2, 425--451. MR2770019
  • Bożejko, Marek; Wysoczański, Janusz. Remarks on $t$-transformations of measures and convolutions. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), no. 6, 737--761. MR1863276
  • Bryc, Wlodzimierz. Classical versions of $q$-Gaussian processes: conditional moments and Bell's inequality. Comm. Math. Phys. 219 (2001), no. 2, 259--270. MR1833804
  • Bryc, Włodzimierz. Free exponential families as kernel families. Demonstratio Math. 42 (2009), no. 3, 657--672. MR2554960
  • Bryc, Włodek. Markov processes with free-Meixner laws. Stochastic Process. Appl. 120 (2010), no. 8, 1393--1403. MR2653258
  • Chihara, T. S. An introduction to orthogonal polynomials. Mathematics and its Applications, Vol. 13. Gordon and Breach Science Publishers, New York-London-Paris, 1978. xii+249 pp. ISBN: 0-677-04150-0 MR0481884
  • Ejsmont, Wiktor. Laha-Lukacs properties of some free processes. Electron. Commun. Probab. 17 (2012), no. 13, 8 pp. MR2900354
  • Ejsmont W.: Characterizations of some free random variables by properties of conditional moments of third degree. To be published in Journal of Theoretical Probability, (2013).
  • Hiai, Fumio; Petz, Dénes. The semicircle law, free random variables and entropy. Mathematical Surveys and Monographs, 77. American Mathematical Society, Providence, RI, 2000. x+376 pp. ISBN: 0-8218-2081-8 MR1746976
  • Hora, Akihito; Obata, Nobuaki. Quantum probability and spectral analysis of graphs. With a foreword by Luigi Accardi. Theoretical and Mathematical Physics. Springer, Berlin, 2007. xviii+371 pp. ISBN: 978-3-540-48862-0 MR2316893
  • Michna, Z. Approximation of a symmetric $\alpha$-stable Lévy process by a Lévy process with finite moments of all orders. Studia Math. 180 (2007), no. 1, 1--10. MR2302007
  • Meixner, J. Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion. J. London Math. Soc. S1-9 no. 1, 6. MR1574715
  • 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
  • Saitoh, Naoko; Yoshida, Hiroaki. The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory. Probab. Math. Statist. 21 (2001), no. 1, Acta Univ. Wratislav. No. 2298, 159--170. MR1869728
  • Speicher, Roland. Multiplicative functions on the lattice of noncrossing partitions and free convolution. Math. Ann. 298 (1994), no. 4, 611--628. MR1268597
  • Speicher, Roland. Free probability theory and non-crossing partitions. Sém. Lothar. Combin. 39 (1997), Art. B39c, 38 pp. (electronic). MR1490288
  • Szpojankowski K., Wesol owski J.: Dual lukacs regressions for non-commutative variables. arXiv:1110.3419v1 (2012).
  • Takesaki, Masamichi. Conditional expectations in von Neumann algebras. J. Functional Analysis 9 (1972), 306--321. MR0303307
  • 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

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.