Hyperscaling for oriented percolation in 1+1 space-time dimensions
Date/Time :
12 Feb 2018 16:00 Venue : S17 #04-05 SR2 Speaker : Akira Sakai,
Hokkaido University
Date/Time:12 Feb 2018 16:00Venue: S17 #04-05 SR2Speaker: Akira Sakai , Hokkaido UniversityHyperscaling for oriented percolation in 1+1 space-time dimensionsConsider nearest-neighbor oriented percolation in d+1 space-time dimensions. Let \rho,\eta, \nu be the critical exponents for the survival probability up to time t, the expected number of vertices at time t connected from the space-time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality d \nu >= \eta+2\rho, which holds for all d>=1 and is a strict inequality above the upper-critical dimension 4, becomes an equality for d=1, i.e., \nu=\eta+2\rho, provided existence of at least two among \rho,\eta,\nu. The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin, Tassion and Teixeira (2017).Add to calendar:
