Leírás
Shearer's inequality (1986) concerns the joint entropies of different subsets of any set of random variables. The entropy inequalities of Csóka-Harangi-Virág (2020) are similar, but work only for random variables defined via some shared independent bits. I will give three wildly different applications of these inequalities.
The first is isoperimetric inequalities in Euclidean lattices, with applications to random walks on percolation clusters, from an old paper of mine (2008). The second is the impossibility of guessing the output of a function of many weakly dependent random variables from a sparse sample of the input, from joint work with Pál Galicza (2020-25). The third is work in progress with Endre Csóka and Péter Mester, about understanding how small density factor of i.i.d. percolation clusters in nonamenable groups may look like; this is inspired by the theory of measurable cost of groups.