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RESEARCH INTERESTS.

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

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Publicaciones/Publications

1. O. Arizmendi, S.G.G. Johnston
   Free probability via entropic optimal transport.
   Invent. math. (2026).
   

2. O. Arizmendi, K. Fujie, D. Perales, Y. Ueda
   S-transform in finite free probability
   Advances in Mathematics 489, 110803, 2026
   

3. Arizmendi, O., Hasebe, T., & Kitagawa, Y.
   Free multiplicative convolution with an arbitrary measure on the real line.
   Probability Theory and Related Fields, 1-53. (2026)
   

4. S. Arenas-Velilla, O. Arizmendi, J.E. Paguyo
   Central Limit Theorem for Crossings in Randomly Embedded Graphs.
   J Theor Probab 38, 59 (2025)
   

5. O. Arizmendi, C. Huemer and P. Cano.
   On the number of crossings in a random labelled tree
   XIV Symposium on Probability and Stochastic Processes. SPSP 2023. Progress in Probability, vol 81. Birkh\"auser (2025).
   

6. O. Arizmendi, S. R. Mendoza, J. Vazquez-Becerra
   BMT independence
   Journal of Funcional Analysis, 288(2), 110712. (2025)
   

7. O. Arizmendi, K.Fujie, Y. Ueda
   New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
   International Mathematics Research Notices, 2024(14), 10524-10558.
   

8. O. Arizmendi, G. Cebron, R. Speicher, S. Yin
   Universality of free random variables: atoms for non-commutative rational functions
   Advances in Mathematics, 443, 109595 (2024)
   

9. O. Arizmendi, S. Sigarreta
   The change of vertex energy when joining trees
   Linear Algebra and its Applications, 687, 117-131.
   

10. O. Arizmendi, J. Guerrero
    On the p-Schatten Energy of Bipartite Graphs
    Acta Mathematica Hungarica, 169(2), 503-509.
    

11. O. Arizmendi, T. Hasebe, F. Lehner
    Cyclic independence: Boolean and monotone
    Algebraic Combinatorics
    

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

13. Arizmendi, O., Mingo J. A.
    Second Order Cumulants: second order even elements and R-diagonal elements
    Annales d'Institut Henri Poincare D, 12(2), 265-318.
    

14. S. Arenas-Velilla, O. Arizmendi
    Convergence rate for the number of crossings in a random labelled tree.
    Statistics & Probability Letters 203 (2023)
    

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

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

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

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

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

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

21. 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
    

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

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

24. 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

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

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

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

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

29. 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

30. 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

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

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

33. 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

34. 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,

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

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

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

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

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

40. 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)

41. 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

42. 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

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

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

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

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

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

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

49. 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.

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

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

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

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

54. Arizmendi, O., Perez-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.

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

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    Estudiantes/Students Supervision

    Doctorado / PHD

    • Saul Rogelio Mendoza   (Ph. D., 2024)
    • Santiago Arenas Velilla   (Ph. D., 2022)
    • Ricardo Guerrero   (Ph. D., 2022)
    • Mauricio Salazar Mendez   (Ph. D., 2019)
    • Marco Tulio Gaxiola  (Ph. D., 2017)

    Master

    • Juan Esaul Gonzalez Rangel   (2021)
    • Julian Zazueta Obeso   (2021)
    • Gustavo Adolfo Garcia Gutierrez   (2021)
    • Saul R. Mendoza Jacobo   (2019)
    • Adrian de Jesus Celestino   (2018)
    • Daniel Munoz Georges   (2018)
    • Guillermo Herrera Ramirez   (2018)
    • Daniel Perales Anaya.   (2018)
      
    • Marco Tulio Gaxiola  (2014)

    Licenciatura/Bachelor

    • Jorge Fernandez Hidalgo (2021)
    • Ramon Ivan Garcia alvarez  (2018) Mencion honorifica Sotero Prieto 2019
    • Areli Karina Martinez Tapia  (2018)
    • Jorge Garza Vargas   (2017) Premio Sotero Prieto 2018
    • Saul R. Mendoza Jacobo   (2017)
    • Iris Stephanie Arias Longoria   (2017)
    • Daniel Munoz Georges   (2016)
    • Daniel Perales Anaya.   (2016) Mencion honorifica Sotero Prieto 2017
    • Adrian de Jesus Celestino   (2016) Mencion honorifica Sotero Prieto 2017
    
    
    webpages of some of my coauthors and friends
    • Michael Anshelevich
    • Takahiro Hasebe
    • Franz Lehner
    • Victor Perez Abreu
    • Gelasio Salazar
    • Roland Speicher
    • Pierre Tarrago
    • Carlos Vargas
    
    CURSO ELEMENTOS DE PROBABILIDAD Y ESTADISTICA 2020
    CURSO MODELOS ESTOCaSTICOS 2018
    CURSO PROBABILIDAD Y COMBINATORIA 2019
    DISCRETE MATH 2019
    
    Pinturas 2019
    
    Nuevo! SEMINARIO DE CHARLAS CORTAS