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):
- D. Montealegre, and V. Vu. "Results on preferential attachment graphs", (in preparation).
- A. James, M. Larson, D. Montealegre, A. Salmon, "Union of Random Trees and Applications", (submitted).
- A. Ferber, K. Luh, D. Montealegre, O. Nguyen, "Packing Loose Hamilton Cycles", (to appear in Combinatorics, Probability and Computing).
- A. Ferber, D. Montealegre, V. Vu, "Law of Iterated Logarithm in random graphs", (to appear Random Structures and Algorithms).
- A. Ferber, D. Montealegre, V. Vu, "Random matrices: Law of the iterated logarithm", (submitted).
- 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.
- 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.
- 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.