Are you interested in complex systems, opinion dynamics, or the voter model? Do you have a Master's degree in Physics or Mathematics and a good grasp of statistics and numerical simulation? Would you like to work together with me as your PhD supervisor? If so, apply for a PhD studies at the Institute of Theoretical Physics and Astronomy (part of the Faculty of Physics at Vilnius University). Description of the PhD topic I am offering is provided below.

We have already previously shared a video about the central limit theorem, but recently I have found another neat explanation by StatQuest. I would like to invite you to watch it.

Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. I was given to cover a chapter about the central limit theorem, which reminded me that I had already given a similar presentation while being PhD student myself. While diving into the topic, I have noticed a couple things, which are usually glanced over in a typical statistics handbook. Let me share them with you.

In the previous post we have started simple - with the law of large numbers. In this post, let us consider a natural extension of this result - the central limit theorem.

This year I was invited to give lecture to gifted high school students attending Nacionalinė moksleivių akademija. It was a great experience for me. I hope that my lecture was at least a bit useful and inspiring. You can find the slides here.

Immediately after the lecture I have remembered that have forgotten to make an important philosophical point, and to somewhat contradict the conclusion made by Veritasium in a recent video on power-law distributions.

In the video's thumbnail, one can see a claim that "working hard is not enough." I do agree with this point, but by the end of the video, one of the hosts (Casper) suggests that in a power-law world, it becomes "more important to be persistent than consistent". This interpretation is sound, and the emphasis on persistence seems both intuitive and motivating. That said, it is important to add a nuance to the discussion.

In environments governed by power laws, outcomes are often heavily influenced by chance and/or external factors. As a result, many considerable successes cannot be fully explained by individual qualities such as ability, persistence, or consistency alone. From this perspective, persistence may increase exposure to opportunities, while the ultimate magnitude of success remains strongly shaped by factors outside individual control. The point I am trying to make is well-presented in the Talent vs Luck model.

Similarly, the wealthiest agents in kinetic exchange models with savings are the ones with largest saving propensity. These agents are successful because they contribute to the shared pot the least, while having a chance at receiving an equal share of the pot back.

In an earlier post we have taken a moral formal look at the law of large numbers. But what about the intuition behind this law? I believe this video by Jeremy Blitz-Jones provides a great general level overview of the importance of this law.