CAREER: Stochastic Spatial Systems

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This project focuses on understanding stochastic spatial models in three settings: chemical reactions, viral phages cooperating to attack bacteria, and lesion formation from multiple sclerosis. Traditional modeling approaches often omit randomness and heterogeneity. Such assumptions yield tractable equations but sacrifice salient features of the processes being modeled. Stochastic spatial models provide a more nuanced perspective. Exploring the theoretical frontier will allow us to better harness their untapped potential. This project synergistically incorporates research training for undergraduates, junior researchers, and students who are incarcerated.There is limited understanding of annihilating and coalescing particle systems with asymmetric diffusion rates. Objective One devises new methods, such as couplings and multi-scale percolation constructions, to describe phase-transitions in these systems. Objective Two involves cooperative infection dynamics in spatial Susceptible-Infected models. The emergence of large-scale infections in these models on sparse random graphs and integer lattices will be studied. Objective Three proposes a new modeling paradigm for axon demyelination due to multiple sclerosis. Variants of stochastic growth models such as internal diffusion-limited aggregation and the Eden model will be utilized. The goal is to capture aspects of inflammatory processes that damage the central nervous system by studying the interplay between growth and suppression in these models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.