Diffractive patterns in deep-inelastic scattering and parton genealogy

We report on our recent observation that the occurrence of diffractive patterns in the scattering of electrons off nuclei obeys the same law as the fluctuations of the height of genealogical trees in branching diffusion processes.

Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion

The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, along with the natural boundary and initial conditions, has only the trivial solution, i.e. explosion in finite time does not occur, provided the creation rate does not grow faster than the square power at ∞.