Passage time of the frog model has a sublinear variance

  • Can Van Hao
  • Nakajima Shuta

UNDEFINED

In this paper, we show that the passage time in the frog model on Z d with d ≥ 2 has a sublinear variance. The proof is based on the method introduced in [8] combining with tessellation arguments to estimate the martingale difference. We also apply this method to get the linearity of the lengths of optimal paths.