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, Non-Commutative Probability
  • Probability: Limit Theorems, Random Matrices, Infinite divisibility
  • Combinatorics: Partition sets, Cumulants, Incidence Algebras
  • Graphs: Spectral graph theory, Energy of Graphs, Random Graphs

  • Publicaciones/Publications

    1. O. Arizmendi, J. Guerrero
      On the p-Schatten Energy of Bipartite Graphs
      to appear in Acta Mathematica Hungarica

    2. O. Arizmendi, T. Hasebe, F. Lehner
      Cyclic independence: Boolean and monotone
      to appear in Algebraic Combinatorics

    3. O. Arizmendi, Jorge Garza-Vargas, Daniel Perales
      Finite Free Cumulants: Multiplicative Convolutions, Genus Expansion and Infinitesimal Distributions
      to appear in Transactions of AMS

    4. Arizmendi, O., Mingo J. A.
      Second Order Cumulants: second order even elements and R-diagonal elements
      to appear in Annales d'Institut Henri Poincare D

    5. G. Arizmendi, O. Arizmendi
      The graph energy game
      Discrete Applied Mathematics, Vol. 330, 15 May 2023, Pages 128-140

    6. Arizmendi O. Dominguez Russel E.
      Barabasi-Albert trees are hypoenergetic
      Boletín de la Sociedad Matemática Mexicana volume 28, Article number: 72 (2022)

    7. O. Arizmendi, A. Celestino (2022)
      Monotone cumulant-moment formula and Schröder trees,
      SIGMA (to appear)

    8. Arizmendi, G., & Arizmendi, O. (2022)
      Energy and Randic index of directed graphs.
      Linear and Multilinear Algebra, DOI: 10.1080/03081087.2022.2119193

    9. Arizmendi, O., Perales D.
      A Berry-Esseen type theorem for finite free convolution
      In: López, S.I., Rivero, V.M., Rocha-Arteaga, A., Siri-Jégousse, A. (eds)
      XIII Symposium on Probability and Stochastic Processes. Progress in Probability, vol 75. Birkhäuser, Cham.

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

    11. Arizmendi, O., Mingo J. A.
      The Cyclic Group and the Transpose of an R-cyclic matrix
      Journal of Operator Theory Volume 85, Issue 1, pp. 135-151. Volume dedicated to Dan-Virgil Voiculescu's 70th birthday

    12. Arizmendi, O., A. Celestino
      Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum
      Random Matrices: Theory and Applications 2020, 2150020

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

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

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

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

    17. O. Arizmendi, B.C. Luna Olivera,M. 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

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

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

      Related: Vertex energy of small graphs

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

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

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

    23. O. Arizmendi, O.Juarez-Romero
      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

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

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

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

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

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

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

    30. 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)

    31. 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

    32. 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

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

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

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

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

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

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

    39. 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.

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

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

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

    43. 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).

    44. 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.

    45. 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).


    46. O. Arizmendi, C. Huemer and P. Cano.
      On the number of crossings in a random labelled tree with vertices in convex position
      arXiv: 1902.05223

    47. O. Arizmendi, S. Arenas-Velilla
      Crossings in Randomly Embedded Graphs
      arXiv: 2205.14527

    48. O. Arizmendi, G. Cébron, R. Speicher, S. Yin
      Universality of free random variables: atoms for non-commutative rational functions
      arXiv: 2107.11507

    Estudiantes/Students Supervision

    Doctorado / PHD



    webpages of some of my coauthors and friends

    Pinturas 2019