Wlodzimierz Bryc Professor of Mathematical Sciences

Department of Mathematical Sciences University of Cincinnati PO Box 210025 Cincinnati, OH 45221-0025 Fax: (513) 556 3417

Preprints at ArXiv Suggested Readings

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

Your picture here... Your name goes here... Topic of thesis: Your thesis title goes here... Close According to Bard (2023), three general areas of current interest in probability are: 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. 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. 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. Close ...

1. 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.
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.
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.
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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.
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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.
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27. A sensitivity estimate for Boolean functions, with Wlodzimierz Smolenski, Computers Math. Applic. 28 (1994) 45-52.
    
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.
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.
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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. 
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    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.
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42. 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
    
44. On a class of free Levy laws related to a regression problem, with Marek Bozejko, Journal of Functional Analysis 236 (2006), 59-77.
    
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. 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. 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. 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.
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58. Askey-Wilson polynomials, quadratic harnesses and martingales, with Jacek Wesolowski, Ann. Probab., 38 (2010) pp. 1221--1262
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.
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.
63. Bridges of quadratic harnesses , with Jacek Wesolowski, Electron. J. Probab. 17 (2012), no. 105, 1-25.
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.
68. Fock space realizations of some classical Markov processes, with Wiktor Ejsmont, Probability and Mathematical Statistics Vol. 33, (2013), pp. 301-313.
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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.)
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70. On Cauchy-Stieltjes Kernel Families, with Raouf Fakhfakh and Abdelhamid Hassairi. Journ. Multivariate Anal. Vol. 124 (2014) pp. 296-312.
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,
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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.
75. The local structure of $q$-Gaussian processes, with Yizao Wang, Probab. Math. Stat. 36 (2016) pp. 335-352.
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
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. 2169–2194. https://doi.org/10.1214/18-AIHP945 Prix AIHPB
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
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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
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
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
84. 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. ALEA, Lat. Am. J. Probab. Math. Stat. 19, 1329–1351 (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 353–389 (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
88. Limit theorems for random Motzkin paths near boundary, with Yizao Wang [Dec-2022-April 2023] . Bernoulli, to appear.
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89. Pitman's discrete $2M-X$ theorem for arbitrary initial laws and continuous time limits with Jacek Wesolowski [Feb-April 2023]
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90. Fluctuations of random Motzkin paths II, with Yizao Wang. ALEA, Lat. Am. J. Probab. Math. Stat. 21, 73-94 (2024).
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91. Limits of Random Motzkin paths with KPZ related asymptotics with Alexey Kuznetsov and Jacek Wesolowski.
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    [Apr 2023 - Jan 2024].
92. A two-line representation of stationary measure for open TASEP, with Pavel Zatitskii [Nov 2023-March2024]
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Preprint form only

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).