14:00 - 15:00, October 23, 2024 (Wednesday) Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
Critical Point for Oriented Percolation Noe Kawamoto (NCTS)
Abstract
We consider nearest-neighbor oriented percolation defined on the lattice . For each pair of points, we can define a bond by, which is independently open with probability with .
It is well known that oriented percolation exhibits a phase transition as the parameter varies around a critical pointwhich is model-dependent. As to infinity, coverges to 1. However, the best estimate for provided by Cox and Durret (Math. Proc. Camb. Phil. Soc. (1983)) give upper and lower bounds, but do not yield an explicit expression for . In this talk, we investigate the exact expression for when , in a way that , where to are constants. The proof relies on the lace expansion, which is one of the most powerful tool to analyze the mean-field behavior of statistical-mechanical models in high dimensions.
