Georgia Institute of Technology College of Sciences

The emergence of large connected structures in networks has been a central topic in random graph theory since its inception, forming a foundation for understanding fundamental processes such as the spread of influence or epidemics, and the robustness of networked systems. The field witnessed significant growth from the early 2000s, fueled by a surge in experimental work from statistical physics that introduced fascinating concepts such as universality. Broadly speaking, universality suggests that the formation of a giant component in random graphs often depends primarily on macroscopic statistical properties like the degree distribution. In the theoretical literature, two universality classes have emerged, both closely related to Aldous’ seminal work on critical random graphs and the theory of multiplicative coalescents. In this talk, I will present a third universality class that emerges in the setting of percolation on random graphs with infinite-variance degree distributions. The new universality class exhibits fundamentally different behavior compared to multiplicative coalescents and reveals surprising phenomena concerning the width of the critical window—phenomena that were unforeseen in the substantial physics literature on this topic. Based on joint work with Shankar Bhamidi and Remco van der Hofstad.