Together with Ivailo Hartarsky I have written a short book whose goal is to provide an introduction to the mathematical theory of interacting particle systems with kinetic constraints a.k.a. Kinetically Constrained Models (or just KCM), a topic lying at the intersection of probability and statistical mechanics (and definitely one of my favourite topics!). The book is intended to be readable for both mathematicians and physicists and will be edited by Springer in the series Springer Briefs in Mathematical Physics. A preprint of the manuscript may be found here arXiv:2412.13634

... but what are KCM and why do I care for them?

KCM are a (vast) class of interacting particle systems with stochastic dynamics on discrete lattices. They were introduced by physicists in the 1980's to model the liquid-glass transition, a longstanding open problem in condensed matter physics.
In the last twenty years KCM have had a flourishing life also in the probability community. Indeed, despite their simplicity, they pose very challenging mathematical problems requiring the development of several novel tools. Moreover they reserve some nice surprises: their extremely slow and anomalous dynamics makes the correct analysis of numerical results extremely tricky and their peculiar behavior has sometimes fooled the physicists intuition, leaving to mathematicians the (admittedly satisfying ;) ) role of correcting physicists results/conjectures. Last but not least, KCM have deep connections to other mathematical fields, notably to bootstrap percolation type cellular automata, which make their study even more intriguing.
The goal of our book is to provide an introduction to this field accessible both to mathematicians and physicists providing not only an account of the most important results and open problems but also conveying the key ideas behind some new mathematical tools which have been introduced to handle with KCM dynamics.