Welcome to Carlos Vargas' personal webpage

Ginibre animation

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I am a Professional Mathematician / Jr. Software Developer / Amateur Screen-Saver Artisan.

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, posets and their combinatorial Moebius functions.

Recently I became interested in eigenvalue dynamics for matrix processes associated with Ginibre matrices.

Pre-print

  1. Vargas C.
    Eingenvalue collisions for periodic matrix families associated with Ginibre matrices.
    (2025).

Publications

  1. 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).
  2. 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).
  3. Vargas, C.
    A general solution to (free) deterministic equivalents.
    Contemporary Mathematics (AMS/SMM) vol 709, pp 28 (2018).
  4. Arizmendi, O., Vargas C.
    Norm convergence in non conmutative central limit theorems.
    Contemporary Mathematics (AMS/SMM), vol. 657, pp 63-73 (2016).
  5. Arizmendi, O., Nechita I., Vargas, C.
    On the asymptotic distribution of block-modified random matrices.
    Journal of Mathematical Physics 57, 015216, (2016).
  6. Arizmendi O., Hasebe, T., Lehner, F., Vargas, C.
    Relations between cumulants in noncommutative probability.
    Advances in Mathematics Volume 282, pp 56–92, (2015)
  7. 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).
  8. 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).
  9. Speicher, R., Vargas C.
    Free deterministic equivalents, renctangular random matrix models and operator-valued free probability.
    Random Matrices: Theory and Applications 01, 1150008, (2012).
  10. 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

Organized Conferences