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Bootstrap Percolation On Random Geometric Graphs, Alyssa Whittemore
Bootstrap Percolation On Random Geometric Graphs, Alyssa Whittemore
Department of Mathematics: Dissertations, Theses, and Student Research
Bootstrap Percolation is a discrete-time process that models the spread of information or disease across the vertex set of a graph. We consider the following version of this process:
Initially, each vertex of the graph is set active with probability p or inactive otherwise. Then, at each time step, every inactive vertex with at least k active neighbors becomes active. Active vertices will always remain active. The process ends when it reaches a stationary state. If all the vertices eventually become active, then we say we achieve percolation.
This process has been widely studied on many families of graphs, deterministic …