Rotationally invariant first passage percolation: Concentration and scaling relations

For rotationally invariant first passage percolation on the plane, we use a multi-scale argument to prove stretched exponential concentration of the passage times at the scale of the standard deviation. Our results are proved for several standard rotationally invariant models of first passage percolation, e.g., Riemannian FPP, Voronoi FPP and the Howard-Newman model. As a consequence, we prove a version of the scaling relations between the passage times fluctuation and transversal fluctuations of geodesics. These are the first such unconditional results.