Universality in two-dimensional enhancement percolation

F. Camia

Research output: Contribution to JournalArticleAcademicpeer-review


We consider a type of dependent percolation introduced in [2], where it is shown that certain "enhancements" of independent (Bernoulli) percolation, called essential, make the percolation critical probability strictly smaller. In this study we first prove that, for two-dimensional enhancements with a natural monotonicity property, being essential is also a necessary condition to shift the critical point. We then show that (some) critical exponents and the scaling limit of crossing probabilities of a two-dimensional percolation process are unchanged if the process is subjected to a monotonic enhancement that is not essential. This proves a form of universality for all dependent percolation models obtained via a monotonie enhancement (of Bernoulli percolation) that does not shift the critical point. For the case of site percolation on the triangular lattice, we also prove a stronger form of universality by showing that the full scaling limit [12,13] is not affected by any monotonic enhancement that does not shift the critical point. © 2008 Wiley Periodicals, Inc.
Original languageEnglish
JournalRandom Structures and Algorithms
Issue number3
Publication statusPublished - 2008

Bibliographical note



Dive into the research topics of 'Universality in two-dimensional enhancement percolation'. Together they form a unique fingerprint.

Cite this