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

Fax: (513) 556 3417


Probability Theory: quadratic harnesses, random matrices, large deviations, strong-mixing dependence.

Books and Monographs

  1. Normal distribution: characterizations with applications, Lecture Notes in Statistics vol 100, Springer 1995. [DVI 1995] Corrected Version [PDF 2008]

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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According to Bard (2023), three general areas of current interest in probability are:

  1. Probabilistic modeling of complex systems. This is a rapidly growing area of research, with applications in many fields, including physics, biology, finance, and computer science. Probabilistic models can be used to describe the behavior of complex systems that are too difficult to model deterministically. For example, probabilistic models have been used to study the behavior of financial markets, the spread of diseases, and the evolution of biological populations.
  2. Understanding the behavior of stochastic processes. Stochastic processes are models of systems that evolve over time in a probabilistic manner. They are used in a wide variety of applications, such as finance, physics, and biology. There is a great deal of active research in understanding the behavior of stochastic processes, such as the properties of their equilibria and the ways in which they can be used to make predictions.
  3. Applying probability theory to real-world problems. Probability theory has a wide range of applications in the real world, such as risk management, decision making, a nd cryptography. There is a great deal of active research in applying probability theory to new and challenging problems.

6th Cincinnati Symposium, May 2024

Math Papers

  1. Stanislaw Kwapien, Knoxville 2003 On the conditional expectation with respect to a sequence of independent $\sigma$-fields, with Stanislaw 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 Richard Bradley, Journ. Multiv. Anal. 16 (1985), 335-367. Rick Bradley, Cincinnati, May 2004
  7. A characterization of infinite gaussian sequences by conditional moments, with Agnieszka 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 Richard C. Bradley & Svante Janson), in New Perspectives in Theor. App. Stat, ed. M. Puri, Wiley, 421-437, 1987.
  10. On dominations between measures of dependence, with Richard Bradley & Svante 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 Pawel Szabowski, Bull Polish Acad. Sci. 38 (1990), 209-218.
  16. The Central Limit Theorem for the Tukey's 3R Smoother , with Magda 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 Wlodzimierz 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 Wlodzimierz Smolenski, Statist. Probab. Letters. 15 (1992) 41-46.
  23. On the large deviation principle for a quadratic functional of the autoregressive process, with Wlodzimierz Smolenski, Statist. Probab. Letters 17 (1993) 281-285. Wlodek Smolenski, Cincinnati, 1988
  24. A remark on the connection between the large deviation principle and the central limit theorem, Statist. Probab. Lett. 18 (1993) 253-256.
  25. On probabilities of linear sets, with Wlodzimierz Smolenski, Journ. Mult. Anal. 45(1993) 25-33.
  26. On the convergence of averages of mixing sequences, with Wlodzimierz Smolenski, Journ. Theoret. Probab. 6 (1993) 473-483. Wlodek Smolenski Tomek Bielecki  Chicago, 1992
  27. A sensitivity estimate for Boolean functions, with Wlodzimierz Smolenski, Computers Math. Applic. 28 (1994) 45-52. Wlodek Smolenski Cincinnati, 1991
  28. On large deviations of empirical measures for stationary Gaussian processes, with Amir Dembo, Stoch. Process. Appl. 58 (1995) 23-34.
  29. On Gaussian random measure generated by empirical distributions of independent random variables, with Wlodzimierz 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 Amir 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 Amir 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 Statist. Probability Letters, Volume: 47, Issue: 4, May 1, 2000, pp. 391-394
  34. Variational representations of Varadhan functionals , with Harold 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 Victor Kaftal, Proc. Amer. Math. Soc. 132 (2004), 523-534. DOI
  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 Amir Dembo and Abram Kagan, Theory of Probability and Its Applications Volume 49, (2005) pp. 132-138.
  41. Probabilistic aspects of Al-Salam--Chihara polynomials, with Wojciech Matysiak and Pawel 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 Jacek 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 Amir Dembo and Tiefeng 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 Marek Bozejko, Journal of Functional Analysis 236 (2006), 59-77. Marek Bozejko, Cincinnati, September
  45. The classical bi-Poisson process: an invertible quadratic harness , with Jacek Wesolowski, Statist. Probability Letters 76 (2006), 1664-1674
  46. Bi-Poisson Process, with Jacek 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 Wojciech Matysiak and Jacek 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 Wojciech Matysiak and Jacek 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 Reza Rashidi Far, Tamer Oraby, and Roland 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 Bernard Bercu, Electronic Comm. Probab. 12 (2007) 184--199. Erratum: Proof of Theorem 1 is incorrect: Lemma 2 was misquoted! (Noticed by Mark Meckes in 2010. Thank you Mark.). "Erratum: Asymptotic results for empirical measures of weighted sums of independent random variables", with Bernard Bercu, Electronic Communications in Probability 2022, Vol. 27, paper no. 23, 1-1. https://doi.org/10.1214/22-ECP464
  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 Marek 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. Large deviations for the leaves in some random trees, with C. David Minda and Sunder Sethuraman, Advances in Applied Probab., 41 (2009), 845-873. At work
  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 Katarzyna 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. Multivariate 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 Wojtek Matysiak, Cincinnati/Lawrensburg, IN,  2006
  74. Infinitesimal generators for a class of polynomial processes with Jacek Wesolowski Studia Mathematica 229 (2015), 73-93. Jacek Wesolowski, 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
  77. Dual representations of Laplace transforms of Brownian excursion and generalized meanders, with Yizao Wang, Statistics and Probability Letters 140 (2018) 77-83. At work in Cincinnati  2018
  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 happyPrix AIHPBhappy
  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 Raouf Fakhfakh - Cincinnatus 2016 Wojciech Mlotkowski Bedlewo 2022
  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 with Yizao Wang,  86 Coffee, Cincinnati,  April 2023
  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 applications to harnesses, with Jacek Wesolowski and Agnieszka Zieba. Colloquium Mathematicum 170 (2022), 211--238 DOI: 10.4064/cm8549-1-2022 Jacek Wesolowski Agnieszka Zieba Bedlewo 2022
  84. Covid-19 On the continuous dual Hahn process Stochastic Processes and their Applications Vol 143 (2022), Pages 185-206 https://doi.org/10.1016/j.spa.2021.10.009
  85. Markov limits of steady states of the KPZ equation on an interval, with Alexey Kuznetsov. with Alexey Kuznetsov, Fields Institute April 2022 ALEA, Lat. Am. J. Probab. Math. Stat. 19, 13291351 (2022)
  86. Markov processes related to the stationary measure for the open KPZ equation, with Alexey Kuznetsov, Yizao Wang, and Jacek Wesolowski, Probability Theory Rel. Fields 185, pages 353389 (2023). with Alexey Kuznetsov, Jacek Wesolowski, Yizao Wang,  86 Coffee, Cincinnati,  April 2023 https://doi.org/10.1007/s00440-022-01110-7
  87. From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval, with Yizao Wang and Jacek Wesolowski. Annales de l'Institut Henri Poincare 2023 vol. 59, pages 2257-2284. DOI: 10.1214/22-AIHP1315 W. Bryc, J. Wesolowski, Y. Wang. Cincinnati, Nov 2021
  88. Limit theorems for random Motzkin paths near boundary, with Yizao Wang. . Bernoulli 2024, Vol. 30, No. 3, 2185-2206. DOI: 10.3150/23-BEJ1669 with Yizao Wang at UC  April 2023
  89. Pitman's discrete $2M-X$ theorem for arbitrary initial laws and continuous time limits with Jacek Wesolowski [Feb-April 2023] W. Bryc, J. Wesolowski, Bedlewo, July 2022
  90. Fluctuations of random Motzkin paths II, with Yizao Wang. ALEA, Lat. Am. J. Probab. Math. Stat. 21, 73-94 (2024).
  91. Limits of Random Motzkin paths with KPZ related asymptotics with Alexey Kuznetsov and Jacek Wesolowski. Cincinnati Symphony April 2023 [Apr 2023 - Jan 2024].
  92. A two-line representation of stationary measure for open TASEP, with Pavel Zatitskii [Nov 2023-March2024] Prob Seminar March 2024
  93. In prep., with Joseph Najnudel and Yizao Wang [2024?] At 86, Cincinnati, May 2024

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Preprint form only

    Mourad Ismail, Cincinnati, October 2005
  1. Approximation Operators, Exponential, and q-Exponential Families (with Mourad Ismail) [Dec 2005]
  2. Projection formulas for orthogonal polynomials (with Wojciech Matysiak, Ryszard Szwarc, and Jacek Wesolowski [2006]
  3. Spectra of large block matrices (with Tamer Oraby, Reza Rashidi Far, and Roland Speicher) [2006]

Other Papers

  1. O intensywnosci uszkodzen elementow dzialajacych zaleznie (with Jerzy 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 Adaptive Math Placement (2001-2022).

Wlodzimierz Bryc
University of Cincinnati

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