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
905 Evans Hall
grunbaum [at] math [dot] berkeley [dot] edu
+1 (510) 642-5348
Year Appointed: 
Selected Publications: 
  1. Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L. Quantum Markov
    chains: recurrence, Schur functions and splitting rules. Ann. Henri
    Poincaré 21 (2020), no. 1, 189–239. 81P47 (81S22)
    Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun
    operator and band-time limiting. Comm. Math. Phys. 364 (2018), no. 3,
  3.  Grünbaum, F. Alberto; de la Iglesia, Manuel D. Stochastic LU
    factorizations, Darboux transformations and urn models. J. Appl. Probab.
    55 (2018), no. 3, 862–886. 60J10 (33C45 42C05)

   4.  Grünbaum, F. A.; Velázquez, L. A
generalization of Schur functions: applications to Nevanlinna
functions, orthogonal polynomials, random     walks and unitary and open
quantum walks. Adv. Math. 326 (2018), 352–464.    5. Cedzich,
C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.;
Werner, R. F. The topological classification of one-dimensional
symmetric quantum walks. Ann. Henri Poincaré 19 (2018), no. 2, 325–383.        6.    Grünbaum, Francisco Alberto; Velázquez, Luis The CMV bispectral problem. Int. Math. Res. Not. IMRN 2017, no. 19, 5833–5860.     7.   Castro,
M.; Grünbaum, F. A. Time-and-band limiting for matrix orthogonal
polynomials of Jacobi type. Random Matrices Theory Appl. 6          (2017), no.
4, 1740001, 12 pp.      8.  Grünbaum,
F. A.; Pacharoni, I.; Zurrián, I. Time and band limiting for matrix
valued functions: an integral and a commuting differential           operator.
Inverse Problems 33 (2017), no. 2, 025005, 14 pp.       9.  Grünbaum,
F. Alberto; Vinet, Luc; Zhedanov, Alexei Tridiagonalization and the
Heun equation. J. Math. Phys. 58 (2017), no. 3, 031703,           12 pp.        10.  Cedzich,
C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner,
R. F. Bulk-edge correspondence of one-dimensional               quantum walks. J.
Phys. A 49 (2016), no. 21, 21LT01, 12 pp. 81Q35         11. Cedzich,
C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. A
quantum dynamical approach to matrix Khrushchev's              formulas. Comm. Pure
Appl. Math. 69 (2016), no. 5, 909–957.

          12.  Grünbaum,
F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel Time and band
limiting for matrix valued functions, an example.                 SIGMA Symmetry
Integrability Geom. Methods Appl. 11 (2015), Paper 044, 14 pp. 42C10           13. Grünbaum,
F. Alberto Some noncommutative matrix algebras arising in the
bispectral problem. SIGMA Symmetry Integrability Geom.                Methods Appl. 10
(2014), Paper 078, 9 pp.   

  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, Matrix valued Szegő polynomials and quantum random walks, Comm. Pure Appl. Math. 63 (2010) 464-507
  5. Grünbaum, F. Alberto (2010). An urn model associated with Jacobi polynomials. Commun. Appl. Math. Comput. Sci. 5 55-63. [MR] [GS?]
  6. 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?
  7. 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?]
  8. 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