I have also attended couple of conferences in the end of October. At International Conference on Noise and Fluctuations I got asked a question the gist of which was what would change in my model, if inter-event times would be normally distributed. I would expect that, in the particular case I was talking about, little would change, but let us make sure of that. In this post, we will take a look at point process, and we will revisit a more complicated topic I talked about later on.

A member of our research group gave a talk on Nobel prize awarded in 2021 at 45th Lithuanian National Physics Conference. Habil. dr. B. Kaulakys talked about the research for which the prize was awarded and how this research relates to works by Lithuanian physicists (mostly our group) and mathematicians. We invite you to watch it, but note that the recording is in Lithuanian. The slides, also in Lithuanian, are available here.

Recording was made by the organizers of the conference. The full recording of the special session is available on the Facebook page of Faculty of Physics at Vilnius University. See this post, if you are interested.

In the previous post we have seen that introducing memory into the memory-less Poisson process makes things very complicated. But we haven't yet still seen 1/f noise. So now let us consider power-law distributed inter-event times!

Over the last few posts we have been talking about the power spectral density of different random processes. We have used the fact that it is a modulus of the signal's Fourier transform squared. But what is the meaning of the power spectral density? Watch the video by "Iain Explains" below for some intuition.

In the previous post we have seen that the Poisson process generates white noise, which is not unexpected consequence of exponential distribution being a limit of geometric distribution. So, if we use non-exponential inter-event time distribution, we introduce memory into the process. As the distribution of inter-event times is no longer exponential, we now have not a Poisson process, but a point process.