Submitted to the Annals of Applied Probability MULTI-SCALE LIPSCHITZ PERCOLATION OF INCREASING EVENTS FOR POISSON RANDOM WALKS By
Submitted to the Annals of Applied Probability MULTI-SCALE LIPSCHITZ PERCOLATION OF INCREASING EVENTS FOR POISSON RANDOM WALKS By
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提交给《应用概率年鉴》 泊松随机游走增加事件的多尺度利普希兹渗透
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Alexandre O. Stauffer
中科院分区：
文献类型：
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作者：
Peter Gracar;Alexandre O. Stauffer
考虑由Z诱导的具有均匀椭圆随机导数的图。在时间0处，将粒子的泊松点过程放置在Z上，并让它们执行独立的简单随机行走。将图形细分为I∈Z索引的立方体，并将时间细分为τ索引的间隔。给出一个局部事件E(I，τ)，它只依赖于由立方体I和时间间隔τ给出的时空区域内的粒子，我们证明了存在一个Lipschitz连通胞腔曲面(I，τ)，它将原点与E(i，τ)所在的无穷大分开。这为在这种情况下证明需要多尺度论证的结果提供了一个直接适用和健壮的框架。例如，这使我们能够证明感染在颗粒中以正速度传播。
Consider the graph induced by Z, equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Z and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i ∈ Z and tessellate time into intervals indexed by τ . Given a local event E(i, τ) that depends only on the particles inside the space time region given by the cube i and the time interval τ , we prove the existence of a Lipschitz connected surface of cells (i, τ) that separates the origin from infinity on which E(i, τ) 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.