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Abstract
Consider the graph induced by Z^{d}, equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Z^{d} and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i ∈ Z^{d} 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 multiscale argument. For example, this allows us to prove that an infection spreads with positive speed among the particles.
Original language  English 

Pages (fromto)  376433 
Number of pages  58 
Journal  Annals of Applied Probability 
Volume  29 
Issue number  1 
Early online date  5 Dec 2018 
DOIs  
Publication status  Published  28 Feb 2019 
Bibliographical note
The text has been improved throughout and the proofs clarifiedKeywords
 math.PR
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Dive into the research topics of 'Multiscale Lipschitz percolation of increasing events for Poisson random walks'. Together they form a unique fingerprint.Projects
 1 Finished

Early Career Fellowship  Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A.
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council