On the connection problem for Painlevé I
Résumé
We study the dependence of the tau function of Painlev\'e I equation on the
generalized monodromy of the associated linear problem. In particular, we
compute connection constants relating the tau function asymptotics on five
canonical rays at infinity. The result is expressed in terms of dilogarithms of
cluster type coordinates on the space of Stokes data.