RESEARCH INTERESTS.
Publicaciones/Publications
-
O. Arizmendi, S. R. Mendoza, J. Vazquez-Becerra
BMT independence
to appear in Journal of Funcional Analysis
-
O. Arizmendi, K.Fujie, Y Ueda
New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
to appear in IMRN
-
O. Arizmendi, G. Cebron, R. Speicher, S. Yin
Universality of free random variables: atoms for non-commutative rational functions
to appear in Advances in Mathematics
-
O. Arizmendi, S. Sigarreta
The change of vertex energy when joining trees
to appear in Linear Algebra and its Applications
-
O. Arizmendi, J. Guerrero
On the p-Schatten Energy of Bipartite Graphs
to appear in Acta Mathematica Hungarica
-
O. Arizmendi, T. Hasebe, F. Lehner
Cyclic independence: Boolean and monotone
to appear in Algebraic Combinatorics
-
O. Arizmendi, Jorge Garza-Vargas, Daniel Perales
Finite Free Cumulants: Multiplicative Convolutions, Genus Expansion and Infinitesimal Distributions
to appear in Transactions of AMS
-
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
-
G. Arizmendi, O. Arizmendi
The graph energy game
Discrete Applied Mathematics, Vol. 330, 15 May 2023, Pages 128-140
-
Arizmendi O. Dominguez Russel E.
Barabasi-Albert trees are hypoenergetic
Boletin de la Sociedad Matematica Mexicana volume 28, Article number: 72 (2022)
-
O. Arizmendi, A. Celestino (2022)
Monotone cumulant-moment formula and Schröder trees,
SIGMA (to appear)
-
Arizmendi, G., & Arizmendi, O. (2022)
Energy and Randic index of directed graphs.
Linear and Multilinear Algebra, DOI: 10.1080/03081087.2022.2119193
-
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.
-
Arizmendi, G., & Arizmendi, O. (2021)
Energy of a graph and Randic index.
Linear Algebra and its Applications, 609, 332-338.
-
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
-
Arizmendi, O., A. Celestino
Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum
Random Matrices: Theory and Applications 2020, 2150020
-
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).
-
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
- O. Arizmendi, M. Ballesteros, F. Torres-Ayala,
Conditionally Free Reduced Products of Hilbert Spaces.
Studia Mathematica, 254, 23-44
- O. Arizmendi, J. Fernandez-Hidalgo
Graphs of Maximal Energy with Fixed Maximal Degree
MATCH Commun. Math. Comput. Chem, Volume 83 pp. 531-539
-
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
-
O. Arizmendi, T. Hasebe
Limit theorems for free Levy processes.
Electronic Journal of Probability, Volume 23 (2018), paper no. 101, 36 pp.
-
O. Arizmendi, J. Fernandez, O. Juarez-Romero
Energy of a vertex
Linear Algebra and its Applications, Volume 557, 15 November 2018, Pages 464-495
-
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
-
O. Arizmendi
k-divisible random variables in free probability
Advances in Applied Mathematics
Volume 93, February 2018, Pages 1-68
-
O. Arizmendi, D. Perales
Cumulants for finite free convolution
Journal of Combinatorial Theory, Series A
Volume 155, April 2018, Pages 244-266
- 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
-
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,
-
O. Arizmendi, T. Hasebe
Classical Scale Mixtures of Boolean Stable Laws
Transactions of the American Mathematical Society 368 (2016), 4873-4905
-
O. Arizmendi, I. Nechita, C. Vargas
On the asymptotic distribution of block-modified random matrices
Journal of Mathematical Physics 57, 015216 (2016)
-
O. Arizmendi, G. Salazar
Large
area convex holes in random points sets
(2016) SIAM J. Discrete Math., 30(3), 1866–1875.
-
O. Arizmendi, T. Hasebe
Free Subordination and Belinschi-Nica Semigroup
Complex Analysis and Operator Theory 10 (2016), no. 3, 581–603.
-
Arizmendi, O., Vargas, C.
Norm convergence in Non-Commutative Central Limit Theorems: Combinatorial Approach.
Contemporary Mathematics, Volume 657, 2016, 237 pp.
-
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)
-
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
-
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
-
Arizmendi, O., Jaramillo, A.
Convergence of the fourth moment and infinite divisibility: quantitative estimates
Electronic Communications in Probability (2014) 19, 1-12.
-
Arizmendi, O., Hasebe T.
Classical and free infinite divisibility for Boolean stable laws.
Proc. Amer. Math. Soc. 142 (2014), no. 5, 1621–1632.
-
Arizmendi, O. , Vargas C.
Limit theorems and infinite divisibility in non-commutative probability.
Bol. Soc. Mat. Mexicana (3) 19 (2013), no. 2, 139–157.
-
Arizmendi, O.
Convergence of the fourth moment and infinite divisibility
Probab. Math. Statist. 33 (2013), no. 2, 201–212.
-
Arizmendi, O., Belinschi S. T.
Free Infinite Divisibility for Ultrasphericals
Infinite Dimensional Analysis, Quantum Probability and Related Topics. March 2013, Vol. 16, No. 01.
-
Arizmendi, O., Hasebe T., Sakuma N.
On the Law of free Subodinators
ALEA, Lat. Am. J. Probab. Math. Stat. 10 (2), 271-291 (2013)
-
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.
-
Arizmendi, O., Hasebe T.
Semigroups related to Boolean and free convolutions.
Studia Math. 215 (2013), no. 2, 157–185.
-
Arizmendi, O.
Statistics of blocks in k-divisible non-crossing partitions
Electronic. J. Combin. 19 (2), Research Paper 47, (electronic) (2012)
-
Arizmendi, O., Vargas C.
Products of free random variables and k-divisible non-crossing
partitions
Electron. Commun. Probab. 17 (2012) no. 11, 13 pp.
- 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).
- 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.
- 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).
Enviados/Submitted
-
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
-
O. Arizmendi, S. Arenas-Velilla
Crossings in Randomly Embedded Graphs
arXiv: 2205.14527
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
BMT independence
to appear in Journal of Funcional Analysis
New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
to appear in IMRN
Universality of free random variables: atoms for non-commutative rational functions
to appear in Advances in Mathematics
The change of vertex energy when joining trees
to appear in Linear Algebra and its Applications
On the p-Schatten Energy of Bipartite Graphs
to appear in Acta Mathematica Hungarica
Cyclic independence: Boolean and monotone
to appear in Algebraic Combinatorics
Finite Free Cumulants: Multiplicative Convolutions, Genus Expansion and Infinitesimal Distributions
to appear in Transactions of AMS
Second Order Cumulants: second order even elements and R-diagonal elements
to appear in Annales d'Institut Henri Poincare D
The graph energy game
Discrete Applied Mathematics, Vol. 330, 15 May 2023, Pages 128-140
Barabasi-Albert trees are hypoenergetic
Boletin de la Sociedad Matematica Mexicana volume 28, Article number: 72 (2022)
Monotone cumulant-moment formula and Schröder trees,
SIGMA (to appear)
Energy and Randic index of directed graphs.
Linear and Multilinear Algebra, DOI: 10.1080/03081087.2022.2119193
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.
Energy of a graph and Randic index. Linear Algebra and its Applications, 609, 332-338.
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
Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum
Random Matrices: Theory and Applications 2020, 2150020
Subordination methods for free deconvolution.
In Annales de l'Institut Henri Poincare, Probabilites et Statistiques (Vol. 56, No. 4, pp. 2565-2594).
Berry-Esseen type estimate and return sequence for parabolic iteration in the upper half-plane.
International Mathematics Research Notices, , rnz365
Conditionally Free Reduced Products of Hilbert Spaces.
Studia Mathematica, 254, 23-44
Graphs of Maximal Energy with Fixed Maximal Degree
MATCH Commun. Math. Comput. Chem, Volume 83 pp. 531-539
Coulson Integral Formula for the Vertex Energy of a Graph.
Linear Algebra and its Applications, Volume 580, 1 November 2019, Pages 166-183
Limit theorems for free Levy processes.
Electronic Journal of Probability, Volume 23 (2018), paper no. 101, 36 pp.
Energy of a vertex
Linear Algebra and its Applications, Volume 557, 15 November 2018, Pages 464-495
A Berry Esseen type limit theorem for Boolean convolution.
Archiv der Mathematik, July 2018, Volume 111, Issue 1, pp 101–111
k-divisible random variables in free probability
Advances in Applied Mathematics Volume 93, February 2018, Pages 1-68
Cumulants for finite free convolution
Journal of Combinatorial Theory, Series A Volume 155, April 2018, Pages 244-266
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
The exponential map in non-commutative probability
International Mathematical Research Notices. Volume 2017, Issue 17, 1 September 2017, Pages 5302–5342,
Classical Scale Mixtures of Boolean Stable Laws
Transactions of the American Mathematical Society 368 (2016), 4873-4905
On the asymptotic distribution of block-modified random matrices
Journal of Mathematical Physics 57, 015216 (2016)
Large area convex holes in random points sets
(2016) SIAM J. Discrete Math., 30(3), 1866–1875.
Free Subordination and Belinschi-Nica Semigroup
Complex Analysis and Operator Theory 10 (2016), no. 3, 581–603.
Norm convergence in Non-Commutative Central Limit Theorems: Combinatorial Approach.
Contemporary Mathematics, Volume 657, 2016, 237 pp.
On the spectral distributions of distance $k$-graphs of free product graphs.
Infinite Dimensional Analysis, Quantum Probability and Related Topics. 19, 1650017 (2016)
Relations between cumulants in noncommutative probability
Advances in Mathematics Volume 282, 10 September 2015, Pages 56–92
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
Convergence of the fourth moment and infinite divisibility: quantitative estimates
Electronic Communications in Probability (2014) 19, 1-12.
Classical and free infinite divisibility for Boolean stable laws.
Proc. Amer. Math. Soc. 142 (2014), no. 5, 1621–1632.
Limit theorems and infinite divisibility in non-commutative probability.
Bol. Soc. Mat. Mexicana (3) 19 (2013), no. 2, 139–157.
Convergence of the fourth moment and infinite divisibility
Probab. Math. Statist. 33 (2013), no. 2, 201–212.
Free Infinite Divisibility for Ultrasphericals
Infinite Dimensional Analysis, Quantum Probability and Related Topics. March 2013, Vol. 16, No. 01.
On the Law of free Subodinators
ALEA, Lat. Am. J. Probab. Math. Stat. 10 (2), 271-291 (2013)
On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws.
Bernoulli 19 (2013), no. 5B, 2750–2767.
Semigroups related to Boolean and free convolutions.
Studia Math. 215 (2013), no. 2, 157–185.
Statistics of blocks in k-divisible non-crossing partitions
Electronic. J. Combin. 19 (2), Research Paper 47, (electronic) (2012)
Products of free random variables and k-divisible non-crossing partitions
Electron. Commun. Probab. 17 (2012) no. 11, 13 pp.
On free and classical type G distributions
Brazilian Journal of Probability and Statistics 24, 106-127. (2010).
On the non-classical infinite divisibility of power semicircle distributions
Communications on Stochastic Analysis 4, 161-178. (2010). In honor of Gopinath Kallianpur.
The S-transform for symmetric probability measures with unbounded supports
Proceedings of the American Mathematical Society 137, 3057-3066 (2009).
Enviados/Submitted
On the number of crossings in a random labelled tree with vertices in convex position
arXiv: 1902.05223
Crossings in Randomly Embedded Graphs
arXiv: 2205.14527
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)