Parametric Stokes Phenomenon for the Second Painleve Equation

The second Painleve equation with a large parameter (P-II) is analyzed from the viewpoint of the exact WKB analysis. The purpose of this study is to investigate a new kind of Stokes phenomena which we call "parametric Stokes phenomenon", occurring to transseries solutions of (P-II). To analyze the parametric Stokes phenomenon, we introduce the "Voros coefficient" for (P-II) and derive the connection formula for transseries solutions of (P-II) through the analysis of the Voros coefficient. We also show that the connection formula can be derived by completely different method: the isomonodromic deformation.