First-passage percolation (FPP) is a fundamental model in probability theory that has a wide
range of applications to other scientific areas (growth and infection in biology, optimization in …

There are many ways of establishing upper bounds on fluctuations of random variables, but
there is no systematic approach for lower bounds. As a result, lower bounds are unknown in …

For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale
argument to prove stretched exponential concentration of the first passage times at the scale …

Place an obstacle with probability 1-p 1-p independently at each vertex of Z^ d Z d, and run
a simple random walk before hitting one of the obstacles. For d ≥ 2 d≥ 2 and p strictly …

The Euclidean first-passage percolation (FPP) model of Howard and Newman is a
rotationally invariant model of FPP which is built on a graph whose vertices are the points of …

We establish tail estimates for the averaged empirical distribution of edge weights along
geodesics in first-passage percolation on $\mathbb {Z}^ d $. Our upper bounds also come …

In first-passage percolation (FPP), one assigns iid weights to the edges of the cubic lattice
Z^d and analyzes the induced weighted graph metric. If T(x,y) is the distance between …

This monograph resolves—in a dense class of cases—several open problems concerning
geodesics in iid first-passage percolation on $\mathbb {Z}^ d $. Our primary interest is in the …

We consider a model of first passage percolation (FPP) where the nearest-neighbor edges
of the standard two-dimensional Euclidean lattice are equipped with random variables …

We investigate first-passage percolation on the lattice $\Z^ d $ for dimensions $ d\geq 2$.
Each edge $ e $ of the graph is assigned an independent copy of a non-negative random …