PhD defence

Spectral Signatures of Breaking of Ensemble Equivalence

• P. Dionigi

Date

Wednesday 19 June 2024

Time

11:15 - 12:00 hour

Address

Academy Building
Rapenburg 73
2311 GJ Leiden

Supervisor(s)

• Prof.dr. W.T.F. den Hollander
• Prof.dr. D. Garlaschelli
• Prof.dr. M.R.H. Mandjes

Summary

My research explores how we can describe random networks (think of networks like social networks, the internet, or even biological networks) in two different ways and how these descriptions can lead to different results. This difference is what I call Breaking of Ensemble Equivalence (BEE). Imagine you want to describe a network of friends. One way (canonical ensemble) is to say that, on average, each person has a certain number of friends. Another way (microcanonical ensemble) is to say that each person has exactly a certain number of friends. These two methods might sound similar, but they can actually lead to different outcomes. I used a mathematical tool called spectral theory, specifically looking at the largest eigenvalue of a matrix that represents the network. This largest eigenvalue can tell us a lot about the network's structure.
For simple, uniform networks where everything is evenly distributed, I proved that there is a clear difference between the largest eigenvalues in the two descriptions. This difference is a sign of BEE. I extended my study to more complex networks that aren't evenly distributed. I found that the same kind of differences appear, meaning BEE is a widespread phenomenon.
I also ran computer simulations that support my theoretical findings. These simulations confirm that the differences I found in theory also appear in practical scenarios.
In summary, my research shows that how you choose to describe a random network can significantly impact the results you get. This insight is crucial for accurately modeling and understanding complex networks.

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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