Hyperscaling for oriented percolation in 1+1 space-time dimensions 時 間:2017年11月27日 (星期一) 14:10-15:00


Astro-Math Bldg. 202

Day and Time: 

2017-11-27 (Monday) 14:10 - 15:00


Consider 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 $d\nu\ge\eta+2\rho$, which holds for all $d\ge1$, becomes an equality for $d=1$, i.e., $\nu=\eta+2\rho$, provided existence of $\rho$ and at least one of the other two exponents. The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin, Tassion and Teixeira (2017).

Tea Time: 

15:00 - 15:30