Abstract
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 a B-particle. Such systems, when ran in discrete time, are also referred to as parking processes. We show for a broad family of graphs and random walk kernels that augmenting either the size or variability of the initial placements of particles increases the total occupation time by A-particles of a given subset of the graph. A corollary is that the same phenomenon occurs with the total lifespan of all particles in internal diffusion-limited aggregation.
Funding Statement
RB was partially supported by NSF grant DMS-1855516 and the 2020 Baruch College Discrete Math REU. PB was partially supported by NSF grant DMS-1855516. TJ was partially supported by NSF grant DMS-1811952 and PSC-CUNY Award #62628-00 50. MJ was partially supported by NSF grant DMS-1855516.
Citation
Riti Bahl. Philip Barnet. Tobias Johnson. Matthew Junge. "Diffusion-limited annihilating systems and the increasing convex order." Electron. J. Probab. 27 1 - 19, 2022. https://doi.org/10.1214/22-EJP808
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