F. Alberto Grünbaum

Professor Emeritus
Primary Research Area: 
Applied Mathematics
Additional Research Areas: 
Mathematical Analysis
Research Interests: 
Analysis, Probability, Integrable systems, Medical imaging
Contact Information
903 Evans Hall
grunbaum [at] math [dot] berkeley [dot] edu
+1 (510) 642-5348
Year Appointed: 
Selected Publications: 
  1. J. Bourgain, F.A. Grünbaum, L. Velázquez and J. Wilkening; Quantum recurrence of a subspace and operator valued Schur functions, (on line already)  in Comm. Math. Phys. (2014)  arXiv: 1302.7286 v1.
  2. F.A. Grünbaum, L. Velázquez, A. Werner and R. Werner; Recurrence for discrete time unitary evolutions, Comm. Math. Phys. (320) 2013
  3. F.A. Grünbaum, L. Velázquez, The quantum walk of F. Riesz, Foundations of computational mathematics, Budapest 2011, 93-112, London Math. Soc. Lecture Note Ser. 403, Cambridge Univ. Press, Cambridge, 2013.
  4. M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, The CGMV method for quantum walks, Quantum Inf. Process. 11 (2012) 1149-1192.
  5. M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, One-dimensional quantum walks with one defect, Rev. Math. Phys. 24 (2012) 1250002 [52 pages].  
  6. M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, Matrix valued Szegő polynomials and quantum random walks, Comm. Pure Appl. Math. 63 (2010) 464-507.
  7. Grünbaum, F. Alberto (2010). A spectral weight matrix for a discrete version of Walsh's spider. In Topics in operator theory. Volume 1. Operators, matrices and analytic functions Oper. Theory Adv. Appl. 202 253-264 Birkhäuser Verlag Basel. [MR] [GS?]
  8. Grünbaum, F. Alberto (2010). An urn model associated with Jacobi polynomials. Commun. Appl. Math. Comput. Sci. 5 55-63. [MR] [GS?]
  9. Grünbaum, F. Alberto (2009). The Karlin-McGregor formula for a variant of a discrete version of Walsh's spider. J. Phys. A 42 No.45, 454010, 10. [link] [MR] [GS?]
  10. Grünbaum, F. Alberto (2009). Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. In Modern analysis and applications. The Mark Krein Centenary Conference. Vol. 1: Operator theory and related topics Oper. Theory Adv. Appl. 190 267-277 Birkhäuser Verlag Basel. [link] [MR] [GS?]
  11. Durán, Antonio J. and Grünbaum, F. Alberto (2009). Matrix differential equations and scalar polynomials satisfying higher order recursions. J. Math. Anal. Appl. 354 No.1, 1-11. [link] [MR] [GS?]
  12. Grünbaum, F. Alberto (2008). Random walks and orthogonal polynomials: some challenges. In Probability, geometry and integrable systems Math. Sci. Res. Inst. Publ. 55 241-260 Cambridge Univ. Press Cambridge. [MR] [GS?]
  13. Grünbaum, F. Alberto and de la Iglesia, Manuel D. (2008). Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. SIAM J. Matrix Anal. Appl. 30 No.2, 741-761. [link] [MR] [GS?]
  14. Castro, Mirta M. and Grünbaum, F. Alberto (2008). The noncommutative bispectral problem for operators of order one. Constr. Approx. 27 No.3, 329-347. [link] [MR] [GS?]