Financial/Actuarial Mathematics Seminar

Let G_n be a sequence of undirected, n-vertex dense graphs, and G_n(1/n) be the associated percolated random graphs. In this talk, we determine the size of k-core of G_n(1/n) using branching process and theory of dense graph limits. We use two different techniques to show the upper and lower bounds of the size of k-core. Our result can also be used to obtain the threshold of appearance of a k-core of order n. In addition, we obtain a probabilistic result concerning cut-norm and branching process which might be of independent interest. Based on the joint work with Erhan Bayraktar and Suman Chakraborty. Speaker(s): Xin Zhang (UM)