We provide a combinatorial formalism for dealing with the cancellations that have
appeared recently in the context of dispersive PDEs with random initial data. The
main idea is to transform iterated integrals encoded by decorated trees into words via
an arborification map. This provides a formalism alternative to the one of
molecules introduced by Deng and Hani (2023). It allows us to compute the
cancellations coming from wave turbulence and the proof of the invariance of the
Gibbs measure under the dynamics of the three-dimensional cubic wave
equation.
Keywords
arborification, cancellation, decorated tree, dispersive
PDE, word
