Imagine a simple game. You are presented two envelopes and asked to choose one of them. Then you are shown that the envelope you have selected contains \( x \) monies. Then you are told that the other envelope contains either \( 10 x \) or \( \frac{x}{10} \) monies (with equal probabilities). Should you open the other envelope and take the monies in it? Or should you keep your original envelope?

The video below has participated in "Summer of Math Exposition" competition in 2021. It explains various ways to define and solve the two envelope problem and provides a valuable lesson on expected values.

FiveThirtyEight has an interesting column, Riddler column, which I follow with great interest. In this post we will take a look at bowling percolation puzzle formulated as Riddler Classic puzzle for August 5th post.

How many birds could potentially fit on a wire? Well it depends on how "jumpy" they are. In [1] it was shown that density of birds is approximately \( \frac{1}{2 r + 1} \) in the steady state regime (here \( r \) is the tolerance distance of the birds). In this post we provide an interactive applet for the two dimensional case (field).

How many birds could potentially fit on a wire? Well it depends on how "jumpy" they are. In [1] a group of researchers looked at this problem from multi-dimensional perspective. In this post we will examine simplest - one-dimensional case.

So, the summer has ended and a new academic year has started. This summer I finally was able to get almost three weeks of decent vacation time (even did some unsuccessful fishing and stargazing). Thus I have recovered enough energy to prepare some new content for Physics of Risk. So Physics of Risk lives again!

Now, this semester we will take a look at a quite a few statistical puzzles. Some of the upcoming posts will be inspired by recent preprints I have seen on the arXiv this summer, while others will be solutions to various Riddler problems published on fivethirtyeight.com.

I was also considering writing a couple of posts on point processes (related to my newest paper [1]), random telegraph noise (currently still working on this paper) and non-Markovian opinion dynamics (seen couple of interesting seminars this summer). Though these will likely have to wait until after the new year.

Happy new academic year!

References

• A. Kononovicius, R. Kazakevičius, B. Kaulakys. Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes. Chaos, Solitons & Fractals 162: 112508 (2022). doi: 10.1016/j.chaos.2022.112508. arXiv:2205.07563 [cond-mat.stat-mech].