In a recent video Veritasium talked about a topic close to our heart - power-law distributions! It is a neat video, which covers a lot of important models and concepts. And it also explains the implications of power-law distributions on everyday life. We invite you to watch it, and maybe revisit our posts on some of the models discussed in the video (such as The Saint Petersburg paradox, Ising model, self-organized criticality models, Barabasi-Albert model).

When writing our recent article [1], we (I and Rytis) had argued about the relationship between having stable voter base (zealots) and imposing boundary conditions on the noisy voter model. This post explores the subtle differences between these notions.

Happy New Year! It is time for the traditional post about our last year's yield. And its still quite good. Though this year, I received some help from my colleague Vygintas Gontis who wrote four posts on macroeconomics and prepared one interactive app.

Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk (as of the end of 2025). The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts containing an interactive app.

We have started the year with various modifications of the Colonel Blotto game. This series of posts culminated in Colonel Blotto moving to an adjacent field of sports. Next we have discussed periodic polling effects and information delay in the noisy voter model [1]. While in the autumn, we have had couple of posts on various assorted topics.

What's next? Still, I am bit overwhelmed and have no concrete plans, but occasionally I'll post something interesting.

References

• A. Kononovicius, R. Astrauskas, M. Radavičius, F. Ivanauskas. Delayed interactions in the noisy voter model through the periodic polling mechanism. Physica A 652: 130062 (2024). doi: 10.1016/j.physa.2024.130062. arXiv:2403.10277 [physics.soc-ph].

In this Numberphile video prof. Marcus du Sautoy talks about mathematics behind the board game he likes to play with his kids. What a better way to spend winter holidays, than playing board games? Watch the video not only to gain competitive edge, but also to see how serious mathematics (and physics) can be applied to a fun casual activity.

Over the last few posts I have been writing about variety of research conducted by a group based in University of Catania. I have covered some of their models illustrating various often counter-intuitive effects of randomness within social systems. This time let us talk about how a certain degree of randomness could benefit our political life [1].