Wlodzimierz Bryc
Professor of Mathematical Sciences
Department of Mathematical Sciences
University of Cincinnati
PO Box 210025
Cincinnati, OH 45221-0025

Fax: (513) 556 3417

RESEARCH INTERESTS


Probability Theory: non-commutative probability, large deviations, weak dependence, characterizations of stochastic processes.

Books and Monographs


  1. Normal distribution: characterizations with applications, Lecture Notes in Statistics vol 100, Springer 1995. [DVI 1995] Corrected Version [PDF 2005]

PhD Students


Tamer Oraby [PhD 2008]
Thesis: Spectra of Random Block-Matrices and Products of Random Matrices

Andoniaina Josoa Rarivoarimanana [PhD 2014]
Thesis: Unbalanced Urn Models and Applications
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Math Papers


  1. Stanislaw Kwapien, Knoxville 2003 On the conditional expectation with respect to a sequence of independent $\sigma$-fields (with S. Kwapien), Z. Wahrscheinlichk. 46 (1979), 221-225.
  2. On the approximation theorem of I. Berkes and W. Philipp, Demonstr. Math. 15(1982), 807-816.
  3. A remark on continuous independent functions, Ann. Univ. Sci. Budapestinensis 26 (1983), 13-16.
  4. On almost sure convergence and integrability of sums of weakly dependent random vectors, Rev. Roumaine de Math. Pures et Appl. 28 (1983), 265-271.
  5. Conditional expectation with respect to dependent $\sigma$-fields, Proceedings of VII conference on Probab., Brasov, Romania, 1984, 409-411. (refereed)
  6. Multilinear forms and measures of dependence between random variables (with R. Bradley), Journ. Multiv. Anal. 16 (1985), 335-367. Rick Bradley, Cincinnati, May 2004
  7. A characterization of infinite gaussian sequences by conditional moments (with A. Plucinska), Sankhya A vol. 47(1985), 166-173.
  8. Some remarks on random vectors with nice enough behaviour of conditional moments, Bull. Polish Acad. Sci. 33(1985), 677-683.
  9. Remarks on the foundations of measures of dependence (with R. Bradley & S. Janson), in New Perspectives in Theor. App. Stat, ed. M. Puri, Wiley, 421-437, 1987.
  10. On dominations between measures of dependence (with R. Bradley & S. Janson), Journ. Multiv. Anal. 23(1987), 312-329.
  11. A characterization of the Poisson process by conditional moments, Stochastics 20(1987), 17-26.
  12. Trajectories of Gaussian processes and interpolation of Banach spaces, Stoch. Processes Appl. 25 (1987), 257-263.
  13. Remarks on properties of probability distributions determined by conditional moments, Probab. Th. Rel. Fields 78 (1988), 51-62.
  14. On the large deviation principle by the asymptotic value method, in: Diffusion Processes and Related Problems in Analysis, Vol I, ed. M. Pinsky, Birkhäuser, Boston 1990, 447-472. (refereed)
  15. Some characteristic of normal distribution by conditional moments (with P. Szabowski), Bull Polish Acad. Sci. 38 (1990), 209-218.
  16. The Central Limit Theorem for the Tukey's 3R Smoother (with M. Peligrad), Statist. Probab. Lett. 13 (1991), 29-37. Magda Peligrad, Cincinnati, Dec 31 2003
  17. On the large deviation principle for stationary weakly dependent random fields, Ann. Probab. 20 (1992), 1004-1030.
  18. On Large Deviations for Uniformly Strong Mixing Sequences, Stoch. Proc. Appl. 41 (1992), 191-202.
  19. On a measure of symmetry for stationary random sequences, Rocky Mount. Math. Journ 22 (1992), 471-476.
  20. On bivariate distributions with rotation invariant absolute moments, Sankhya A 54 (1992) 432-439.
  21. Moment conditions for almost sure convergence of series of weakly correlated random variables (with W. Smolenski), Proc. Amer. Math. Soc. 119 (1993) 629-635. Tomek Bielecki Joanna Mitro Wlodek Smolenski Evanston, 1992
  22. On the stability problem for conditional expectation (with W. Smolenski), Stat. Probab. Letters. 15 (1992) 41-46.
  23. On the large deviation principle for a quadratic functional of the autoregressive process ( with W. Smolenski), Stat. Probab. Letters 17 (1993) 281-285.
  24. A remark on the connection between the large deviation principle and the central limit theorem, Stat. Probab. Lett. 18 (1993) 253-256.
  25. On probabilities of linear sets (with W. Smolenski), Journ. Mult. Anal. 45(1993) 25-33.
  26. On the convergence of averages of mixing sequences (with W. Smolenski), Journ. Theoret. Probab. 6 (1993) 473-483. Wlodek Smolenski Tomek Bielecki  Chicago, 1992
  27. A sensitivity estimate for Boolean functions, (with W. Smolenski) Computers Math. Applic. 28 (1994) 45-52.
  28. On large deviations of empirical measures for stationary Gaussian processes, with A. Dembo, Stoch. Process. Appl. 58 (1995) 23-34.
  29. On Gaussian random measure generated by empirical distributions of independent random variables, with W. Smolenski, Demonstratio Mathematica XXVIII (1995) 733-738.
  30. Conditional moment representations for dependent random variables Electronic Journal of Probability 1 (1996) paper no 7 pages 1-14 Local Copy
  31. Large deviations and strong mixing, with A. Dembo, Annales de l'I.H.P. Probabilitiés & Statistiques 32 (1996) 549-569. Amir Dembo, Stanford Linear Accelerator, 2005
  32. Large deviations for quadratic functionals of Gaussian process (with A. Dembo) Journal of Theoretical Probability 10 (1997) pp. 307-332 (PDF of Expanded version: IMA Preprint Series No. 1179)
  33. Specifying bivariate distributions by polynomial regressions Statistics & Probability Letters, Volume: 47, Issue: 4, May 1, 2000, pp. 391-394
  34. Variational representations of Varadhan functionals (with H. Bell) Proc. Amer. Math. Soc. 129 (2001), 2119-2125. Harry Bell November 2003
  35. Stationary fields with linear regressions Ann. Probab. 29 (2001), 504-519
  36. Stationary Markov chains with linear regressions, Stoch. Proc. Appl. 93 (2001), pp. 339-348.
  37. Classical versions of q-Gaussian processes: conditional moments and Bell's inequality, Comm. Math. Phys., 219 (2001), pp. 259-270.
  38. Victor Kaftal September 2003 Strong mixing coefficients for non-commutative Gaussian processes (with V. Kaftal). Proc. Amer. Math. Soc. 132 (2004), 523-534.
  39. Large deviations of bivariate empirical measures for two systems coupled by a symmetric interaction. Journ. Theoret. Probab. 16 (2003), 935-955.
  40. On the maximum correlation coefficient (with A. Dembo and A. Kagan) Theory of Probability and Its Applications Volume 49, (2005) pp. 132-138.
  41. Probabilistic aspects of Al-Salam--Chihara polynomials (with W. Matysiak and P. Szablowski) Proc. Amer. Math. Soc. 133 (2005), 1127-1134. Pawel Szablowski Jacek Wesolowski Wojciech Matysiak, Warsaw March 2003
  42. Jacek Wesolowski Lawrenceburg, February 2004 Conditional moments of q-Meixner processes (with J. Wesolowski) [Corrected Version](Theorem 4.2) Probab. Theory Rel. Fields 131 (2005), 415-441.
  43. Spectral measure of large random Hankel, Markov and Toeplitz matrices (with A. Dembo and T. Jiang) Ann. Probab. 34 (2006), 1-38. Expanded version from ArXiv Amir Dembo, me and Tiefeng Jiang. Minneapolis, August 2005
  44. On a class of free Levy laws related to a regression problem, (with M. Bozejko) Journal of Functional Analysis 236 (2006), 59-77. Marek Bozejko, Cincinnati, September
 2003
  45. The classical bi-Poisson process: an invertible quadratic harness (with J. Wesolowski) Statistics & Probability Letters 76 (2006), 1664-1674
  46. Bi-Poisson Process (with J. Wesolowski), Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 10, No. 2 (2007) 277-291.
  47. Jacek
Wesolowski and Wojtek Matysiak, Cincinnati, August 2004 Quadratic harnesses, q-commutations, and orthogonal martingale polynomials (with W. Matysiak and J. Wesolowski) Trans. Amer. Math. Soc. 359 (2007), no. 11, 5449--5483.
  48. Computing moments of free additive convolution of measures Applied Mathematics and Computation, 194 (2007), 561-567.
  49. The bi-Poisson process: a quadratic harness (with W. Matysiak and J. Wesolowski) Ann. Probab., 36 (2008), 623-646.
  50. Reza Rashidi Far, Tamer
Oraby, me, Roland Speicher. SAMSI, Sept 2006 On slow-fading MIMO systems with non-separable correlation (with R. Rashidi Far, T. Oraby, and R. Speicher) IEEE Transactions on Information Theory, Volume 54, Issue 2, Feb. 2008, pp 544-553.
  51. Asymptotic results for empirical measure of weighted sums of independent random variables (with B. Bercu) Electronic Comm. Probab. 12 (2007) 184--199. Erratum: Proof of Theorem 1 is incorrect: Lemma 2 is misquoted! (Noticed by Mark Meckes in 2010. Thank you Mark.).
  52. Asymptotic normality for traces of polynomials in independent complex Wishart matrices Probab. Theor. Rel. Fields, 140 (2008) 383-405
  53. Compound real Wishart and q-Wishart matrices. Intern. Math. Research Notices 2008: rnn079-42.
  54. Cincinnati  2007 A quadratic regression problem for two-state algebras with application to the Central Limit Theorem (with M. Bozejko) Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12 (2009), 231-249.
  55. Duality of real and quaternionic random matrices (with Virgil Pierce) Electronic Journal Probab. Vol. 14 (2009), Paper no. 17, pages 452--476.
  56. Free Exponential Families as Kernel Families Demonstr. Math., XLII (2009) 657-672 arxiv version
  57. At work Large deviations for the leaves in some random trees (with C. David Minda and Sunder Sethuraman) Advances in Applied Probab., 41 (2009), 845-873.
  58. Askey-Wilson polynomials, quadratic harnesses and martingales (with Jacek Wesolowski) Ann. Probab., 38 (2010) pp. 1221--1262 Tunisia 2008
  59. A remark on the maximum eigenvalue for circulant matrices. (with Sunder Sethuraman) In: "High Dimensional Probabilities V: The Luminy Volume", IMS Collections Vol. 5 (2009) 179-184. Cincinnati/Wyoming  2009
  60. Markov processes with free Meixner laws Stoch. Proc. Appl., 120 (2010) pp. 1393--1403.
  61. Free Quadratic Harness (with Wojciech Matysiak, and Jacek Wesolowski), Stoch. Proc. Appl. 121 (2011) 657-671
  62. One-sided Cauchy-Stieltjes Kernel Families (with Abdelhamid Hassairi) Journ. Theoret. Probab. 24 (2011) pp. 577--594. Cincinnati  2009
  63. Bridges of quadratic harnesses (with Jacek Wesolowski) Electron. J. Probab. 17 (2012), no. 105, 1-25. Tunisia 2008
  64. Quadratic harnesses from generalized beta integrals in "Noncommutative Harmonic Analysis with Applications to Probability III", ed. M. Bozejko, A. Krystek, L. Wojakowski. Banach Center Publications Vol 96 (2012) pp. 67-79.
  65. Stitching pairs of Levy processes into Harnesses, with Jacek Wesolowski. Stoch. Proc. Appl. Volume 122 (2012) pp. 2854-2869
  66. On integrability of quadratic harnesses. Demonstratio Mathematica 45 (2012) 275--282.
  67. Meixner matrix ensembles (with Gerard Letac) Journ. Theoret. Probab. 26 (2013) 107-152. Anger  2009
  68. Fock space realizations of some classical Markov processes, with Wiktor Ejsmont. Probability and Mathematical Statistics Vol. 33, (2013), pp. 301-313. Torun  2013
  69. Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations (with Kasia Bryc and Jack Silverstein) Theoretical Population Biology 89 (2013) 34-43. Corrected version (Oct 2017 - Corrected values M=120 N=2500 in numerical example in Section 3.1 and new proof of Lemma 2.)
    Cincinnati  2010
  70. On Cauchy-Stieltjes Kernel Families, with Raouf Fakhfakh and Abdelhamid Hassairi. Journ. Mutlivariate Anal. Vol. 124 (2014) pp. 296-312. Cincinnati  2016
  71. Infinitesimal generators of q-Meixner Markov processes with Jacek Wesolowski, Stochastic Processes and their Applications 124/1 (2014), pp. 915-926
  72. On integration with respect to the $q$-Brownian motion Stats Probab Letters 94(2014) 257-266
  73. Wilson's 6-j laws and stitched Markov processes, with Wojciech Matysiak. Teorya Veroyatn. Primen. 60 (2015) 333-356. http://dx.doi.org/10.4213/tvp4622
  74. Infinitesimal generators for a class of polynomial processes with Jacek Wesolowski Studia Mathematica 229 (2015), 73-93. Bedlewo  2016
  75. The local structure of $q$-Gaussian processes, with Yizao Wang, Probab. Math. Stat. 36 (2016) pp. 335-352. Cincinnati  2016
  76. Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses, with Jacek Wesolowski Journal of Statistical Physics 167 (2017), 383-415. DOI: 10.1007/s10955-017-1747-5 Columbus  2017 At work in Cincinnati  2018
  77. Dual representations of Laplace transforms of Brownian excursion and generalized meanders, with Yizao Wang Statistics and Probability Letters 140 (2018) 77-83.
  78. Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries, with Yizao Wang. Annales de l'Institut Henri Poincare 55 (2019) pp. 21692194. https://doi.org/10.1214/18-AIHP945 happyPrizehappy
  79. Cauchy-Stieltjes families with polynomial variance functions and generalized orthogonality, with Raouf Fakhfakh and Wojciech Mlotkowski. Probability and Mathematical Statistics 39 (2019) pp 237-258. PDF https://doi.org/10.19195/0208-4147.39.2.1
  80. Fluctuations of random Motzkin paths, with Yizao Wang Advances in Applied Mathematics 106 (2019) 96-116, https://doi.org/10.1016/j.aam.2019.02.003
  81. On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case with Marcin Swieca, Journal of Statistical Physics, 177 (2019), pp. 252-284 https://doi.org/10.1007/s10955-019-02367-4 Cincinnati Train Station  2019
  82. Singular values of large non-central random matrices, with Jack Silverstein, Random Matrices: Theory and Applications, Vol. 9, (2020) 2050012 (32 pages) https://doi.org/10.1142/S2010326320500124 Raleigh  2017
  83. Flows in near algebras with probabilistic applications, with Jacek Wesolowski and Agnieszka Zieba Covid-19


Preprint form only

    Mourad Ismail, Cincinnati, October 2005
  1. Approximation Operators, Exponential, and q-Exponential Families (with M. Ismail) [Dec 2005]
  2. Projection formulas for orthogonal polynomials (with W. Matysiak, R. Szwarc, and J. Wesolowski [2006]
  3. Spectra of large block matrices (with T. Oraby, R. Rashidi Far, and R. Speicher) [2006]

Other Papers

  1. O intensywnosci uszkodzen elementow dzialajacych zaleznie (with J. Rudnicki) in Polish, Zag. Ekspl. Maszyn 1979
  2. Decoding a scrambled text : a hands-on project to illustrate Sampling and Variability Journal Statist. Education, Volume 7, Number 2 (July 1999) .
  3. A uniform approximation to the right normal integral, Applied Mathematics and Computation, 127 (2002), pp. 365-374. with online-only Addendum

CGI activities

Multi Level Math Placement


Address:
Wlodzimierz Bryc
University of Cincinnati

WWW: http://homepages.uc.edu/~brycwz