Local dynamical heterogeneity in glass formers

We study the local dynamical fluctuations in glass-forming models of particles embedded in $d$-dimensional space, in the mean-field limit of $d\to\infty$. Our analytical calculation reveals that single-particle observables, such as squared particle displacements, display divergent fluctuations around the dynamical (or mode-coupling) transition, due to the emergence of nontrivial correlations between displacements along different directions. This effect notably gives rise to a divergent non-Gaussian parameter, $\alpha_2$. The $d\to\infty$ local dynamics therefore becomes quite rich upon approaching the glass transition. The finite-$d$ remnant of this phenomenon further provides a long sought-after, first-principle explanation for the growth of $\alpha_2$ around the glass transition that is \emph{not based on multi-particle correlations}.