The asymptotic shape theorem for generalized first passage percolation
2010 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 38, no 2, 632-660 p.Article in journal (Refereed) Published
We generalize the asymptotic shape theorem in first passage percolation on Z(d) to cover the case of general semimetrics. We prove a structure theorem for equivariant semimetrics on topological groups and an extended version of the maximal inequality for Z(d)-cocycles of Boivin and Derriennic in the vector-valued case. This inequality will imply a very general form of Kingman's subadditive ergodic theorem. For certain classes of generalized first passage percolation, we prove further structure theorems and provide rates of convergence for the asymptotic shape theorem. We also establish a general form of the multiplicative ergodic theorem of Karlsson and Ledrappier for cocycles with values in separable Banach spaces with the Radon-Nikodym property.
Place, publisher, year, edition, pages
2010. Vol. 38, no 2, 632-660 p.
First passage percolation, cocycles, subadditive ergodic theory
IdentifiersURN: urn:nbn:se:kth:diva-13945DOI: 10.1214/09-AOP491ISI: 000275938300007ScopusID: 2-s2.0-77953553228OAI: oai:DiVA.org:kth-13945DiVA: diva2:328522
QC 201007052010-07-052010-07-052011-01-14Bibliographically approved