International cooperative research on

Classical and Noncommutative Gaussian Processes

This page describes research activities partially supported by the National Science Foundation under Grants No. 03-32062 (2003-2006) and No. 05-04198 (2005-2008) Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Related Publications

• R. Speicher Combinatorial theory of the free product with amalgamation and operator-valued free probability theory (Habilitationsschrift) Memoir of the AMS 627 (1998) table of contents, introduction, chapter 1, chapter 2, chapter 3, chapter 4, chapter 5, references
• Saitoh, Naoko; Yoshida, Hiroaki
  • A q-deformed Poisson distribution based on orthogonal polynomials. J. Phys. A 33 (2000), no. 7, 1435--1444.
  • Saitoh, Naoko; Yoshida, Hiroaki q-deformed Poisson random variables on q-Fock space. J. Math. Phys. 41 (2000), no. 8, 5767--5772.
• Michael Anshelevich:
  • Partition-Dependent Stochastic Measures and q-Deformed Cumulants DOCUMENTA MATHEMATICA, Vol. 6 (2001), 343-384
  • q-Levy processes
  • Appell polynomials and their relatives
  • Free Matringale Polynomials J. Funct. Anal. 201 (2003), 228-261
  • Linearization coefficients for orthogonal polynomials using stochastic processes[2003]
• Marek Bozejko
  • M. Bozejko and R. Speicher. Interpolations between bosonic and fermionic relations given by generalized Brownian motions. Math. Z., 222(1):135--159, 1996.
  • M. Bozejko, B. Kummerer and R. Speicher. q-Gaussian Processes: Non-commutative and Classical Aspects Commun. Math. Phys. 185, 129 – 154 (1997)
  • Marek Bozejko, Roland Speicher. Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces Math. Ann. 300 (1994), 97-120.
  • M. Bozejko and M. Guta. Functors of white noise associated to characters of the infinite symmetric group. Comm. Math. Phys. 229(2):209--227, 2002.
  • Marek Bozejko, Michael Leinert, Roland Speicher. Convolution and Limit Theorems for Conditionally Free Random Variables Pac. J. Math. 175 (1996), 357-388
  • Marek Bozejko, W. Bryc, On a class of free Levy laws related to a regression problem Journal of Functional Analysis 236, 59-77 (2006).
  • M. Bozejko, W. Bryc A quadratic regression problem for two-state algebras with application to the Central Limit Theorem, submitted
• W. Bryc
  • W. Bryc. Stationary fields with linear regressions Ann. Probab. 29 (2001), 504-519.
  • W. Bryc. Stationary Markov chains with linear regressions, Stoch. Proc. Appl. 93 (2001), pp. 339-348.
  • Sharper versions of main results are in
    • W. Matysiak and P. Szablowski, Ann. Probab. 30 (2002), no. 3, 1486--1491.
    • W. Matysiak and P. Szablowski, [preprint 2003]
  • W. Bryc Classical versions of q-Gaussian processes: conditional moments and Bell's inequality, Comm. Math. Phys., 219 (2001), pp. 259-270.
  • W. Bryc and V. Kaftal. Strong mixing coefficients for non-commutative Gaussian processes Proc. Amer. Math. Soc. 132 (2004), 523-534.
  • W. Bryc, W. Matysiak and P. Szablowski. Probabilistic aspects of Al-Salam-Chihara polynomials Proc. Amer. Math. Soc. 133 (2005), 1127-1134
  • W. Bryc, J. Wesolowski. Conditional moments of q-Meixner processes Probab. Theory Rel. Fields 131 (2005), 415-441.
  • W. Bryc, J. Wesolowski. Bi-Poisson Process Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 10, No. 2 (2007) 277-291.
  • W. Bryc, W. Matysiak and J. Wesolowski Quadratic harnesses, q-commutations, and orthogonal martingale polynomials Trans. Amer. Math. Soc. 359 (2007), no. 11, 5449--5483.
  • W. Bryc, J. Wesolowski Classical bi-Poisson process: an invertible quadratic harness Statistics & Probability Letters 76 (2006), 1664-1674
  • W. Bryc W. Matysiak and J. Wesolowski The bi-Poisson process: a quadratic harness Ann. Probab., 36 (2008), 623-646.
  • Computing moments of free additive convolution of measur$ Applied Mathematics and Computation, 194 (2007), 561-567.
  • W. Bryc, M. Ismail Approximation Operators, Exponential, q-Exponential, and Free Exponential Families [Dec 2005]
  • W. Bryc, M. Ismail Cauchy kernel Families [2006]
  • Asymptotic normality for traces of polynomials in independent complex Wishart matrices Probab. Theor. Rel. Fields, 140 (2008) 383-405
  • On slow-fading MIMO systems with non-separable correlation (with R. Rashidi Far, T. Oraby, and R. Speicher) IEEE Transactions on Information Theory, 54 (2008), pp 544-553
  • Compound real Wishart and q-Wishart matrices. Intern. Math. Research Notices 2008: rnn079-42.
• J. Wesolowski.
  • J. Wesolowski Stochastic processes with linear conditional expectation and quadratic conditional variance.Probab. Math. Statist. (Wroclaw) 14 (1993), 33--44