Octavio Arizmendi Echegaray picture of me

Dr. Octavio Arizmendi Echegaray

Investigador Titular "B", SNI: Nivel III

Página personal / Personal website
CIMAT, Apdo. Postal 402, Guanajuato, Gto. 36000, México
(52) (473) 27155 Ext 4501, Oficina I-306
Correo electrónico: octavius@cimat.mx


  • Functional Analysis: Operator Algebras, Free Probability.
  • Probability: Limit Theorems, Random Matrices, Infinite divisibility
  • Combinatorics: Partition sets, Cumulants, Incidence Algebras
  • Graphs: Spectral graph theory, Energy of Graphs, Random Graphs



    1. Arizmendi, O., Perales D.
      A Berry-Esseen type theorem for finite free convolution

    2. Arizmendi, G., & Arizmendi, O. (2021)
      Energy of a graph and Randic index. Linear Algebra and its Applications, 609, 332-338.

    3. Arizmendi, O., Mingo J. A.
      The Cyclic Group and the Transpose of an R-cyclic matrix
      Journal of Operator Theory pp. 135-151. Volume dedicated to Dan-Virgil Voiculescu's 70th birthday

    4. Arizmendi, O., A. Celestino
      Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum
      Random Matrices: Theory and Applications (online ready)

    5. Arizmendi, O., Tarrago, P., Vargas, C.
      Subordination methods for free deconvolution.
      In Annales de l'Institut Henri Poincaré, Probabilités et Statistiques (Vol. 56, No. 4, pp. 2565-2594).

    6. Arizmendi, O., Salazar, M. ,J. C. Wang
      Berry-Esseen type estimate and return sequence for parabolic iteration in the upper half-plane.
      International Mathematics Research Notices, , rnz365

    7. Arizmendi O. , Ballesteros M. , Francisco Torres-Ayala F.,
      Conditionally Free Reduced Products of Hilbert Spaces.
      Studia Mathematica, 254, 23-44

    8. O. Arizmendi, J. Fernandez Hidalgo
      Graphs of Maximal Energy with Fixed Maximal Degree
      MATCH Commun. Math. Comput. Chem, Volume 83 pp. 531-539

    9. Arizmendi, O., Luna Olivera B.C., Ramírez Ibáñez, M.
      Coulson Integral Formula for the Vertex Energy of a Graph.
      Linear Algebra and its Applications, Volume 580, 1 November 2019, Pages 166-183

    10. Arizmendi, O., Hasebe T.
      Limit theorems for free Lévy processes.
      Electronic Journal of Probability, Volume 23 (2018), paper no. 101, 36 pp.

    11. Arizmendi, O., Fernandez, J., Juarez-Romero, O.,
      Energy of a vertex
      Linear Algebra and its Applications, Volume 557, 15 November 2018, Pages 464-495

      Related: Vertex energy of small graphs

    12. Arizmendi, O., Salazar, M.
      A Berry Esseen type limit theorem for Boolean convolution.
      Archiv der Mathematik, July 2018, Volume 111, Issue 1, pp 101–111

    13. Arizmendi, O.
      k-divisible random variables in free probability
      Advances in Applied Mathematics Volume 93, February 2018, Pages 1-68

    14. Arizmendi, O., Perales D.
      Cumulants for finite free convolution
      Journal of Combinatorial Theory, Series A Volume 155, April 2018, Pages 244-266

    15. Arizmendi, O., Juarez-Romero, O.
      On bounds for the energy of graphs and digraphs.
      in, Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics, Contemporary Mathematics pp.1-19

    16. Anshelevich, M., Arizmendi, O.
      The exponential map in non-commutative probability
      International Mathematical Research Notices. Volume 2017, Issue 17, 1 September 2017, Pages 5302–5342,

    17. Arizmendi,O, Hasebe, T.
      Classical Scale Mixtures of Boolean Stable Laws
      Transactions of the American Mathematical Society 368 (2016), 4873-4905

    18. Arizmendi, O., Nechita I., Vargas, C.
      On the asymptotic distribution of block-modified random matrices
      Journal of Mathematical Physics 57, 015216 (2016)

    19. Arizmendi, O., Salazar, G.
      Large area convex holes in random points sets
      (2016) SIAM J. Discrete Math., 30(3), 1866–1875. (10 pages)

    20. Arizmendi, O., Hasebe, T.
      Free Subordination and Belinschi-Nica Semigroup
      Complex Analysis and Operator Theory 10 (2016), no. 3, 581–603.

    21. Arizmendi, O., Vargas, C.
      Norm convergence in Non-Commutative Central Limit Theorems: Combinatorial Approach.
      Contemporary Mathematics, Volume 657, 2016, 237 pp.

    22. Arizmendi, O., Gaxiola T.
      On the spectral distributions of distance $k$-graphs of free product graphs.
      Infinite Dimensional Analysis, Quantum Probability and Related Topics. 19, 1650017 (2016)

    23. Arizmendi O., Hasebe, T., Lehner, F., Vargas, C.
      Relations between cumulants in noncommutative probability
      Advances in Mathematics Volume 282, 10 September 2015, Pages 56–92

    24. Arizmendi, O, Gaxiola, T.
      Asymptotic spectral distributions of distance $ k $-graphs of star product graphs
      Progress in Probability, Vol. 69 (2015), XI Symposium on Probability and Stochastic Processes, 47-58

    25. Arizmendi, O., Jaramillo, A.
      Convergence of the fourth moment and infinite divisibility: quantitative estimates
      Electronic Communications in Probability (2014) 19, 1-12.

    26. Arizmendi, O., Hasebe T.
      Classical and free infinite divisibility for Boolean stable laws.
      Proc. Amer. Math. Soc. 142 (2014), no. 5, 1621–1632.

    27. Arizmendi, O. , Vargas C.
      Limit theorems and infinite divisibility in non-commutative probability.
      Bol. Soc. Mat. Mexicana (3) 19 (2013), no. 2, 139–157.

    28. Arizmendi, O.
      Convergence of the fourth moment and infinite divisibility
      Probab. Math. Statist. 33 (2013), no. 2, 201–212.

    29. Arizmendi, O., Belinschi S. T.
      Free Infinite Divisibility for Ultrasphericals
      Infinite Dimensional Analysis, Quantum Probability and Related Topics. March 2013, Vol. 16, No. 01.

    30. Arizmendi, O., Hasebe T., Sakuma N.
      On the Law of free Subodinators
      ALEA, Lat. Am. J. Probab. Math. Stat. 10 (2), 271-291 (2013)

    31. Arizmendi, O., Hasebe T.
      On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws.
      Bernoulli 19 (2013), no. 5B, 2750–2767.

    32. Arizmendi, O., Hasebe T.
      Semigroups related to Boolean and free convolutions.
      Studia Math. 215 (2013), no. 2, 157–185.

    33. Arizmendi, O.
      Statistics of blocks in k-divisible non-crossing partitions
      Electronic. J. Combin. 19 (2), Research Paper 47, (electronic) (2012)

    34. Arizmendi, O., Vargas C.
      Products of free random variables and k-divisible non-crossing partitions
      Electron. Commun. Probab. 17 (2012) no. 11, 13 pp.

    35. Arizmendi, O., Barndorff-Nielsen, O., Pérez-Abreu, V.
      On free and classical type G distributions
      Brazilian Journal of Probability and Statistics 24, 106-127. (2010).

    36. Arizmendi, O., Pérez-Abreu, V.
      On the non-classical infinite divisibility of power semicircle distributions
      Communications on Stochastic Analysis 4, 161-178. (2010). In honor of Gopinath Kallianpur.

    37. Arizmendi, O., Pérez-Abreu, V.
      The S-transform for symmetric probability measures with unbounded supports
      Proceedings of the American Mathematical Society 137, 3057-3066 (2009).


    Estudiantes/Students Supervision

    Doctorado / PHD



    In progress/ En progreso..
    webpages of some of my coauthors and friends

    Pinturas 2019

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