Universität zu Köln

Gracar, Peter ORCID: 0000-0001-8340-8340 and Stauffer, Alexandre (2019). MULTI-SCALE LIPSCHITZ PERCOLATION OF INCREASING EVENTS FOR POISSON RANDOM WALKS. Ann. Appl. Probab., 29 (1). S. 376 - 434. CLEVELAND: INST MATHEMATICAL STATISTICS. ISSN 1050-5164

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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 is an element of 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gracar, Peter UNSPECIFIED orcid.org/0000-0001-8340-8340 UNSPECIFIED Stauffer, Alexandre UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-158669
DOI:	10.1214/18-AAP1420
Journal or Publication Title:	Ann. Appl. Probab.
Volume:	29
Number:	1
Page Range:	S. 376 - 434
Date:	2019
Publisher:	INST MATHEMATICAL STATISTICS
Place of Publication:	CLEVELAND
ISSN:	1050-5164
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPREAD Multiple languages Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/15866