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- W2592012034 abstract "Consider the graph induced by $mathbb{Z}^{d}$, equipped with uniformly elliptic random conductances. At time $0$, place a Poisson point process of particles on $mathbb{Z}^{d}$ and let them perform independent simple random walks. Tessellate the graph into cubes indexed by $iinmathbb{Z}^{d}$ and tessellate time into intervals indexed by $tau$. Given a local event $E(i,tau)$ that depends only on the particles inside the space time region given by the cube $i$ and the time interval $tau$, we prove the existence of a Lipschitz connected surface of cells $(i,tau)$ that separates the origin from infinity on which $E(i,tau)$ holds. This gives a directly applicable and robust framework for proving results in this setting that need a multi-scale argument. For example, this allows us to prove that an infection spreads with positive speed among the particles." @default.
- W2592012034 created "2017-03-16" @default.
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- W2592012034 date "2019-02-01" @default.
- W2592012034 modified "2023-09-23" @default.
- W2592012034 title "Multi-scale Lipschitz percolation of increasing events for Poisson random walks" @default.
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- W2592012034 doi "https://doi.org/10.1214/18-aap1420" @default.
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