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Course Information
Wlodzimierz Bryc
Professor
809B Old Chemistry Building
513-556-4098
wlodzimierz.bryc@uc.edu
Professional Summary
Research Interests: Probability Theory; Classical and non-commutative probability, random matrices, large deviations.
Research Support
(PI) Classical and noncommutative processes, NSF. (05-04198); $69,661.00. Funded 01/07/2005 to 06/30/2008.
(CO-PI) J. Mitro, W. Bryc, R. Chakraborty, M. Peligrad, Cincinnati Symposium on Probability Theory and Applications 2009, NSF. (DMS 0830579 (2009) ); $20,000.00 . Funded 2009 to 12-2009.
(PI) W. Bryc, Research on classical and non-commutative probability, NSF. (DMS 0904720); $118,185.00. Funded 07-2009 to 06-2012.
Peer Reviewed Publications
R. Rashidi Far, T. Oraby, W. Bryc, & R. Speicher (2008). On slow-fading MIMO systems with non-separable correlation. IEEE Transactions on Information Theory, 54(2), 544-553.
W. Bryc (2008). Asymptotic normality for traces of polynomials in independent complex Wishart matrices. Probab. Theor. Rel. Fields, 140, 383-405.
W. Bryc (2008). Compound real Wishart and q-Wishart matrices. Intern. Math. Research Notices, rnn079-42, rnn079-42.
B. Bercu, & W. Bryc (2007). Asymptotic results for empirical measure of weighted sums of independent random variables. Electronic Comm. Probab., 12, 184-199.
W. Bryc, A. Dembo, & T. Jiang (2006). Spectral measure of large random Hankel, Markov and Toeplitz matrices. Ann. Probab., 34, 1-38.
M. Bozejko, & W. Bryc (2006). On a class of free Levy laws related to a regression problem. Journal of Functional Analysis, 236, 59-77.
W. Bryc, & J. Wesolowski (2006). The classical bi-Poisson process: an invertible quadratic harness. Statistics & Probability Letters, 76, 1664-1674.
W. Bryc, A. Dembo, & A. Kagan (2005). On the maximum correlation coefficient. Theory of Probability & Its Applications, 49, 132-138.
W. Bryc, W. Matysiak, & P. Szablowski (2005). Probabilistic aspects of Al-Salam–Chihara polynomials. Proc. Amer. Math. Soc., 133, 1127-1134.
W. Bryc, & J. Wesolowski (2005). Conditional moments of q-Meixner processes. Probab. Theory Rel. Fields, 131, 415-441.
W. Bryc, & V. Kaftal (2004). Strong mixing coefficients for non-commutative Gaussian processes. Proc. Amer. Math. Soc., 132, 523-534.
W. Bryc (2003). Large deviations of empirical measures under symmetric interaction. Journ. Theoret. Probab., 16, 935-955.
W. Bryc (2002). A uniform approximation to the right normal integral. Applied Mathematics and Computation, 127, 365-374.
H. Bell, & W. Bryc (2001). Variational representations of Varadhan functionals. Proc. Amer. Math. Soc., 129, 2119-2125.
W. Bryc (2001). Stationary random fields with linear regressions. Ann. Probab., 29, 504-519.
W. Bryc (2001). Stationary Markov chains with linear regressions. Stoch. Proc. Appl., 93, 339-348.
W. Bryc (2001). Classical versions of q-Gaussian processes: conditional moments and Bell’s inequality. Comm. Math. Phys., 219, 259-270.
A quadratic regression problem for two-state algebras withapplicationto the Central Limit Theorem (with M. Bozejko) InfiniteDimensional Analysis, Quantum Probability and Related Topics, 12 (2009), 231-249.
Duality of real and quaternionic random matrices (with VirgilPierce) Electronic JournalProbab. Vol. 14 (2009), Paper no. 17, pages452--476.
Large deviations for the leaves in somerandom trees (With C. David Minda and Sunder Sethuraman)[Sept2008] Advances in Applied Probab., to appear
Free Exponential Families as Kernel Families Demonstr. Math., to appear.
Books
W. Bryc (1995). Normal distribution: characterizations with applications. Springer.
Paper Presentations
Asymptotic normality for traces of polynomials in independent complex Wishart matrices. Stanford University. 04/16/2007.
Asymptotic normality for traces of polynomials in independent complex Wishart matrices. Special Session on Random Matrices and Non-commutative Probability, Central Section Meeting (Meeting 1025) of the American Mathematical Society. 03/16/2007.
Asymptotic normality for traces of polynomials in independent complex Wishart matrices. University of Sfax, Tunisia. 12/12/2006.
Asymptotic results for empirical measure of weighted sums of independent random variables. AMS Special Session on Limit Theorems of Probability Theory, Cincinnati, OH. 10/21/2006.
Quadratic Harnesses Stochastic Processes and Appl. Paris. 07-2006.
Cauchy kernel families families. St. Flour . 07-2006.
Spectral measure of large random Hankel and Toeplitz matrices. Toulouse, France. 06/13/2006.
Kernel Families for free exponential laws. Warsaw Univ. Techn., Warsaw, Poland. 05/31/2006.
Quadratic Harnesses Plenary talk at 9th Conference on Probability. Bedlewo, Poland. 05-2006.
Spectral measure of large random Hankel and Toeplitz matrices. Queens College, Kingston, Canada. 03/13/2006.
Quadratic harnesses, q-commutations, and orthogonal martingale polynomials. Non-Commutative Harmonic Analysis With Applications To Probability, Bedlewo, Poland. 09-2005.
Conditional moments, gamma, free gamma, and free Poisson laws Wishart and related random matrices. Mahdia, Tunisia. 06-2005.
Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials. University of Washington, Seattle. 04/21/2005.
Markov processes with linear regressions Quantum Probability and Related Topics. Bedlewo, Poland. 06-2004.
Conditional moments of q-Meixner processes Special session in Statistics and Probability. Central AMS Meeting, Ohio University. 03-2004.
Processes with linear regressions and quadratic conditional variances. Queen’s University, Kingston, CA. 09/12/2003.
Stochastic processes with linear conditional expectation variance: q-L´evy processesand quadratic conditional . Seminar talk at Urbana Champaign. 09/04/2003.
Strong mixing coefficients for non-commutative Gaussian processes. Special Session on Weak Dependence in Probability and Statistics, Central Section Meeting (Meeting 985) of the American Mathematical Society, Indiana University Bloomington. 04-2003.
Ibragimov’s hypothesis and non-commutative processes. Warsaw University of Technology. 03/05/2003.
Varadhan’s functional methods in Large Deviations. Warsaw University, Poland. 03-2003.
Varadhan’s functional methods in Large Deviations. N. Copernicus University, Torun, Poland. 02/28/2003.
On processes with quadratic conditional variances. Wroclaw University. 02/20/2003.
Varadhan’s functional methods in Large Deviations. University of M. Curie-Sklodowska, Lublin, Poland. 01/22/2003.
Asymptotic distribution of eigenvalues of random Toeplitz and Hankel matrices. Warsaw University of Technology. 01/15/2003.
Stationary sequences with linear regressions and quadratic conditional variances. Warsaw University of Technology. 01/08/2003.
Stationary sequences with linear regressions and quadratic conditional variances. Stanford University. 09/30/2002.
Covariance estimates for q-Gaussian processes. International workshop on Noncommutative Harmonic Analysis, Wroclaw, Poland . 08-2001.
Stationary sequences with linear regressions. Indiana University, Bloomington. 03-2000.
Honors & Awards
Editorial Board of Journal of Theoretical Probability.
