Welcome to Carlos Vargas' personal webpage
I obtained my PhD in Mathematics in 2015 from Universitaet des Saarlandes, under the supervision of Prof. Dr. Roland Speicher.
I am interested in free and (operator-valued) non-commutative probability, large
random matrices, incidence algebras, cumulants and statistics, posets and their combinatorial Moebius functions, large random graphs and topological spaces,
geometrical and topological data analysis, distributions on manifolds.
Publications
- Diaz-Aguilera C., Gaxiola T., Santos J., Vargas C.
Combinatorics of NC-probability spaces with Independent Constants.
Infinite Dimensional Analysis, Quantum Probability and Related Topics, pp 20 (2022).
- Arizmendi, O., Tarrago, P. Vargas, C.
Subordination methods
for free deconvolution.
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques,
Vol 56, 4, pp 2565-2594 (2020).
- Vargas, C.
A general solution to
(free) deterministic equivalents.
Contemporary Mathematics (AMS/SMM) vol 709, pp 28 (2018).
- Arizmendi, O., Vargas C.
Norm convergence in non
conmutative central limit theorems.
Contemporary Mathematics (AMS/SMM), vol. 657, pp 63-73 (2016).
- Arizmendi, O., Nechita I., Vargas, C.
On
the asymptotic distribution of block-modified random matrices.
Journal of Mathematical Physics 57, 015216, (2016).
- Arizmendi O., Hasebe, T., Lehner, F., Vargas, C.
Relations
between cumulants in noncommutative probability.
Advances in
Mathematics Volume 282, pp 56–92, (2015)
- Belinschi S., Speicher R., Treilhard J., Vargas, C.
Operator-valued
free multiplicative convolution: analytic subordination theory and applications
to random matrix theory.
International Mathematical Research Notices,
(2014).
- Arizmendi, O. , Vargas C.
Limit
theorems and infinite divisibility in non-commutative
probability.
Bol. Soc. Mat. Mex. (3) 19, no. 2, pp 139–157, (2013).
- Speicher, R., Vargas C.
Free
deterministic equivalents, renctangular random matrix models and
operator-valued free probability.
Random Matrices: Theory and Applications 01, 1150008, (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. (2012).
Supervised Students
- Marcos Torres Vivanco (CIMAT, April 2021).
MSc thesis: Estadisticos Topologicos
en el Estudio de Electrocardiogramas.
- Jorge Luis Santos Silva (CIMAT, Jan. 2021).
MSc thesis: Dos que tres propiedades de
cumulantes.
- Saul Rogelio Mendoza Jacobo (CIMAT, Dec. 2019).
MSc thesis: Aplicaciones de la Teoría de Probablidad
Libre a la Teoria de la Informacion Cuántica.
- Carlos Eduardo Diaz Aguilera (CIMAT, Jul. 2019).
MSc thesis: Categorical Independence and
non-commutative distributions for simplicial complexes.
- Gustavo Adolfo Garcia Gutierrez (Universidad de Guanajuato,
Mar. 2019).
BSc thesis: Momentos del Grupo Unitario.
- Saul Rogelio Mendoza Jacobo (Jul. 2017, Universidad Autonoma de
Sinaloa).
BSc thesis: Teoria de Probabilidad
Bi-libre.
Organized Conferences