PhD defence

Approaching equilibrium in a dynamic network

• O. Nagy

Date

Thursday 16 January 2025

Time

13:00 - 14:00 hour

Address

Academy Building
Rapenburg 73
2311 GJ Leiden

Supervisor(s)

• Prof.dr. W.Th.F. den Hollander
• Prof.dr. R.W. van der Hofstad (TU Eindhoven)
• dr. L. Avena (Università Degli Studi Di Firenze)

Summary

Imagine a cup of warm tea, and pour some milk into it. Initially, the liquid might appear chaotic, but eventually it will become uniformly coloured. And, if we were to stir the cup, then the uniform brown colour would develop even faster.

The concepts in the paragraph above extend far beyond the realm of hot beverages. Many random systems exhibit orderly behaviour after a sufficiently large time. If external dynamics are applied, then this approach to equilibrium is generally quicker.

This acceleration of mixing is the core topic of the first two scientific chapters. In both cases, we provide a detailed analysis of the evolution of the total variation distance, a particular way to quantify mixing. In the first chapter, we show that a previously observed trichotomy is actually a hexachotomy–a six-way split. The second chapter shows that the studied system approaches equilibrium through a sudden jump at a random time, which had not been observed before.

The third scientific chapter studies the communication network within a satellite swarm. While in reality the satellites are constantly moving in a complex manner, it is possible instead to study the static network that emerges as a long-term average. These results are interesting for telecommunication engineers, since they can serve as a benchmark for real-world satellite swarms.

Research projects can also produce unexpected by-products. One such by-product of the satellite project is a quantitative method for comparing arbitrary pairs of centrality measures defined on the same graph. This new mathematical object is introduced in the fourth chapter.

PhD dissertations

Approximately one week after the defence, PhD dissertations by Leiden PhD students are available digitally through the Leiden Repository, that offers free access to these PhD dissertations. Please note that in some cases a dissertation may be under embargo temporarily and access to its full-text version will only be granted later.

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