Universality in Random Graphs

Universality is a remarkable phenomenon in probability theory: diverse random systems, despite their microscopic differences, often exhibit the same macroscopic behaviour. The most famous example is the central limit theorem, which allows school children to approximate the chance of flipping more than 60 heads in 100 coin tosses using a normal distribution table—even though the coin itself is not normally distributed.

A similar regularizing effect of randomness can be observed in random networks. This helps explain why broccolis look somewhat like trees—and even like the bronchioles in our lungs. Universality principles are not only mathematically fascinating, but also powerful in applications. If we can show that broccolis, trees, and other random structures satisfying basic assumptions resemble the same random fractal, then we can deduce global properties without needing to fully understand local interactions.

In this talk, I will introduce the idea of universality in random graphs, highlighting its combinatorial, probabilistic, and geometric aspects, and exploring recent developments in this area of research.

The link for participation in the event is the following: fernuni.zoom.us/j/64850280617.

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