Upper bounds on the non-random fluctuations in first passage percolation with low moment conditions

Understand

We consider first passage percolation with i.i.d.

• weights on edges of the d-dimensional cubic lattice.
• Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the d-dimensional cubic lattice, and has moments bigger than 1, we investigate upper bounds on the so-called non-random fluctuations of the model.
• In addition, we give an application of our result to a lower bound for variance of the first passage percolation in the case where the limit shape has flat edges.