I am interested in probability and combinatorics, including randomized algorithms, random graphs and random tree, in particular:
I also like programming and using computer to experiment, prove, and teach mathematics.
Occasionally I play with special functions.
You can find all my research papers on Zotero (most up-to-date), Google Scholar (slightly delayed), and arXiv.
Here are some of my open source software projects on GitHub.
G. Berzunza, X. S. Cai, and C. Holmgren, “The fluctuations of the giant cluster for percolation on random split trees,” arXiv:1902.08109 [math], May 2021 [Online]. [link].
X. S. Cai, P. Caputo, G. Perarnau, and M. Quattropani, “Rankings in directed configuration models with heavy tailed in-degrees,” arXiv:2104.08389 [cs, math], Apr. 2021. link.
X. S. Cai and G. Perarnau, “The diameter of the directed configuration model,” arXiv:2003.04965 [cs, math], Mar. 2020. [link]
X. S. Cai and G. Perarnau, “Minimum stationary values of sparse random directed graphs,” arXiv:2010.07246 [cs, math], Oct. 2020. [link]
X. S. Cai, C. Holmgren, S. Janson, T. Johansson, and F. Skerman, “Inversions in split trees and conditional Galton-Watson trees,” Combinatorics, Probability and Computing, vol. 28, no. 3, pp. 335–364, May 2019, doi: 10/ggmxmh. [pdf]
G. Berzunza, X. S. Cai, and C. Holmgren, “The k-cut model in deterministic and random trees,” The Electronic Journal of Combinatorics, Jul. 2019. [link]
X. S. Cai and L. Devroye, “A study of large fringe and non-fringe subtrees in conditional Galton-Watson trees,” ALEA Lat. Am. J. Probab. Math. Stat., vol. 14, no. 1, pp. 579–611, 2017, doi: 10/ggh2rh. [pdf]
G. Berzunza, X. S. Cai, and C. Holmgren, “The k-Cut Model in Conditioned Galton-Watson Trees,” in 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Dagstuhl, Germany, 2020, vol. 159, p. 5:1-5:10, doi: 10/ggzvz6. [pdf]
X. S. Cai, C. Holmgren, S. Janson, T. Johansson, and F. Skerman, “Inversions in split trees and conditional Galton-Watson trees,” in 29th international conference on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms (AofA 2018), Dagstuhl, Germany, 2018, vol. 110, p. 15:1-15:12, doi: 10/ggmnn6. [pdf]
Cutting resilient networks. [slides]
A study of large fringe and non-fringe subtrees in conditional Galton-Watson trees. Sweden Probabilistic Midwinter Meeting 2017, Meeting of the Catalan, Spanish, Swedish Math Societies, RS&A 2017. [slides]
The conferences and workshops which I have attended or plan to attend.