ON THE DISTRIBUTION FUNCTION OF AREA AND PERIMETER FOR PLANAR POISSON LINE PROCESS

The paper and the candidate solution both derive the kinetic transport–integral equations for a moving secant line in a planar Poisson line field, pass to a one-end Volterra equation with sine kernel after Laplace transforms, and reduce it to a second-order ODE Y'' + G Y = ν (with a Riccati reduction). The core derivations and objects (event kernels, hazards G1/G2, the T-coefficient, and the sine-convolution identity) match. The paper contains some typographical inconsistencies (e.g., tan vs. cot and 1/cos vs. 1/sin), while the model omits the ∂/∂l advection term in its displayed multi-variable PDEs and introduces a nonstandard “local” ∂/∂P term inside Q_F. However, these do not affect the main shared result (the ODE reduction), for which their proofs are substantially the same.