Studies from Eindhoven University of Technology Provide New Data on Probability Research

摘要

2011 JUL 4 - (VerticalNews.com) -- According to the authors of a study fromrnEindhoven, Netherlands, "For critical bond-percolation on high-dimensional torus, this paperrnproves sharp lower bounds on the size of the largest cluster, removing a logarithmic correctionrnin the lower bound in Heydenreich and van der Hofstad (Comm Math Phys 270(2):335-358,rn2007). This improvement finally settles a conjecture by Aizenman (Nuclear Phys B 485(3):551-rn582, 1997) about the role of boundary conditions in critical high-dimensional percolation, and itrnis a key step in deriving further properties of critical percolation on the torus."