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We study the rate of convergence in the Shape Theorem of first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are stated for a given time and complements recent work by the same author, in which the rate of convergence was studied from the standard spatial perspective.
Consider first passage percolation with identical and independent weight distributions and first passage time ${rm T}$. In this paper, we study the upper tail large deviations $mathbb{P}({rm T}(0,nx)>n(mu+xi))$, for $xi>0$ and $x eq 0$ with a time co
We study first-passage percolation where edges in the left and right half-planes are assigned values according to different distributions. We show that the asymptotic growth of the resulting inhomogeneous first-passage process obeys a shape theorem,
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $LL^2$-formula relating the initial measure with the last-passage percolation time. This formul
We study the time constant $mu(e_{1})$ in first passage percolation on $mathbb Z^{d}$ as a function of the dimension. We prove that if the passage times have finite mean, $$lim_{d to infty} frac{mu(e_{1}) d}{log d} = frac{1}{2a},$$ where $a in [0,inf
We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for