caa a22 4500 445391103 CHVBK 20180317143047.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10955-011-0329-1 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0329-1 Carstens Sebastian Mathematisches Institut der LMU, Theresienstr. 39, 80333, Munich, Germany aut Non-coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation [Elektronische Daten] [Sebastian Carstens] This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on $\{0,1\}^{\mathbb {Z}^{2}}$ with the following properties: (a) a single infinite 0cluster exists almost surely, (b) at most one infinite 1∗cluster exists almost surely, (c) certain probabilities regarding 1∗clusters are bounded away from zero. Second, the coexistence of an infinite 1∗cluster and an infinite 0cluster has probability zero when the underlying probability measure is ergodic with respect to translations, positively associated, and satisfies the finite energy condition. The third result analyzes the typical structure of infinite clusters of both types in the absence of positive association. Namely, under a slightly sharpened finite energy condition, the existence of infinitely many disjoint infinite self-avoiding 1∗paths follows from the existence of an infinite 1∗cluster. The same holds with respect to 0paths and 0clusters. Springer Science+Business Media, LLC, 2011 Dependent site percolation nationallicence Zhang's argument nationallicence Infinite cluster nationallicence Infinite path nationallicence Bounded energy nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1223-1237 0022-4715 144:6<1223 2011 144 10955 https://doi.org/10.1007/s10955-011-0329-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0329-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Carstens Sebastian Mathematisches Institut der LMU, Theresienstr. 39, 80333, Munich, Germany aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1223-1237 0022-4715 144:6<1223 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer