Research

My area of research is Probabilistic Combinatorics. In particular, I like to study random graph models and random algorithms. Lately, I have been diving more into spectral properties of these objects.


Here is a list of my publications (last updated August 2017):

  1. D. Montealegre, and V. Vu. "Results on preferential attachment graphs", (in preparation).
  2. A. James, M. Larson, D. Montealegre, A. Salmon, "Union of Random Trees and Applications", (submitted).
  3. A. Ferber, K. Luh, D. Montealegre, O. Nguyen, "Packing Loose Hamilton Cycles", (to appear in Combinatorics, Probability and Computing).
  4. A. Ferber, D. Montealegre, V. Vu, "Law of Iterated Logarithm in random graphs", (to appear Random Structures and Algorithms).
  5. A. Ferber, D. Montealegre, V. Vu, "Random matrices: Law of the iterated logarithm", (submitted).
  6. A. Fujiwara, J. Gibson, M. Jenssen, D. Montealegre, V. Ponomarenko, A. Tenzer, "Arithmetic of Congruence Monoids". Communications in Algebra 44 (8) 2016, pp. 3407-3421.
  7. M. Jenssen, D. Montealegre, V. Ponomarenko, "Irreducible Factorization Lengths and the Elasticity Problem within $\mathbb{N}$". American Mathematical Monthly 120 (4) 2013, pp. 322-328.
  8. F. De Terán, F.M. Dopico, N. Guillery, D. Montealegre, N. Reyes, "The solution of the equation $AX+X^\star B=0$". Linear Algebra and its Applications 438 (7), 2817-2860.