Abstract: In this talk I will discuss a family of Gibbsian measures on the set of Laguerre tessellations. These measures may be used to provide a systematic approach for constructing Gibbsian solutions to Hamilton-Jacobi PDEs by exploring the Eularian description of the shock dynamics. Such solutions depend on kernels satisfying kinetic-like equations reminiscent of the Smoluchowski model for coagulating and fragmenting particles.