Abstract
In percolation theory the critical probability Pc(G) of an infinite connected graph G is defined as the supremum of those values of the occupation probability for which only finite clusters occur. An interesting question is the following: is each number between 0 and 1 the critical probability of some graph? It is shown that the answer is positive. A remarkable intermediate result is that for an important class of graphs the following holds: for each p>or=Pc(G) there exists a subgraph of G with critical probability equal to p.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
