Diffusion-limited annihilating systems and the increasing convex order

We consider diffusion-limited annihilating systems with mobile A-particles and stationary B-particles placed throughout a graph. Mutual annihilation occurs whenever an A-particle meets B-particle. Such systems, when ran in discrete time, are also referred to as parking processes. show for broad family of graphs random walk kernels that augmenting either the size or variability initial placements particles increases total occupation time by given subset A corollary is same phenomenon lifespan all internal aggregation.