Power Lower Bounds for the Central Moments of the Last Passage Time for Directed Percolation in a Thin Rectangle

Abstract

In directed last passage site percolation with i.i.d.~random weights with finite support over a $n\times \lfloor n^{\alpha }\rfloor$ grid, we prove that for $n$ large enough, the order of the $r$-th central moment, $1\le r<+\infty$, of the last passage time is lower bounded by $n^{r(1-\alpha )/2}$, $0<\alpha <1/3$.

20 pages. This manuscript is not to be published because superseded by the other (arXiv:1810.08270) but posted for making the details available in that particular case

References in corpus (1)

• Limiting shape for directed percolation models