200 Citations
Rates of convergence in first passage percolation with low moment conditions
- Mathematics
- 2013
We consider the first passage percolation with i.i.d.\,weights on edges of a cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability…
A shape theorem and semi-infinite geodesics for the Hammersley model with random weights
- Mathematics
- 2010
In this paper we will prove a shape theorem for the last passage percolation model on a two dimensional $F$-compound Poisson process, called the Hammersley model with random weights. We will also…
Fluctuations of transverse increments in two-dimensional first passage percolation
- MathematicsElectronic Journal of Probability
- 2022
We consider finite geodesics for first passage percolation (FPP) on $\mathbb{Z}^2$ with i.i.d.\ continuous passage times having exponential moments. As has been common in the literature, we assume…
Variance bounds for Gaussian first passage percolation
- Computer Science, Mathematics
- 2021
A proof inspired by Kesten of other basic properties of the new FPP model: an upper bound on the variance in the FPP pseudometric given by the Euclidean distance with a logarithmic factor, and a constant lower bound.
Detecting Cascades from Weak Signatures
- Computer ScienceIEEE Transactions on Network Science and Engineering
- 2018
This work views the detection problem of detecting an infection process in a network as a hypothesis testing problem, devise a new inference algorithm, and analyze its false positive and false negative errors in the high noise regime.
STATIONARY EDEN MODEL ON CAYLEY GRAPHS BY TONĆI ANTUNOVIĆ
- Mathematics
- 2017
We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and…
A HSU–ROBBINS–ERDŐS STRONG LAW IN FIRST-PASSAGE PERCOLATION BY DANIEL AHLBERG
- Mathematics
- 2015
Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these…
Isoperimetry in Two‐Dimensional Percolation
- Mathematics
- 2015
We study isoperimetric sets, i.e., sets with minimal boundary for a prescribed volume, on the unique infinite connected component of supercritical bond percolation on the square lattice. In the limit…
GAUSSIAN CONCENTRATION FOR THE LOWER TAIL IN FIRST-PASSAGE PERCOLATION UNDER LOW MOMENTS
- Mathematics
- 2014
We consider first-passage percolation on the d dimensional cubic lattice for d ≥ 2; that is, we assign independently to each edge a nonnegative random weight with a common distribution and consider…
References
SHOWING 1-10 OF 22 REFERENCES
On the critical behavior of the first passage time in d≥3
- Mathematics
- 1991
The first passage times for the Bernoulli percolation problems on the d-dimensional hypercubic lattices are investigated. For all d (and hence for d≥3) it is rigorously established that, in the…
Rounding effects of quenched randomness on first-order phase transitions
- Mathematics
- 1990
Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For…
Some Limit Theorems for Percolation Processes with Necessary and Sufficient Conditions
- Mathematics
- 1981
Noise reduction in Eden models. I
- Physics
- 1987
The authors adapt the multiple hit method of noise reduction introduced earlier for diffusion-limited growth to Eden models A and C on the square lattice. The dynamic scaling is improved…
First-passage percolation on the square lattice. I
- MathematicsAdvances in Applied Probability
- 1977
We consider several problems in the theory of first-passage percolation on the two-dimensional integer lattice. Our results include: (i) a mean ergodic theorem for the first-passage time from (0,0)…
On a Class of Branching Processes on a Lattice with Interactions
- Mathematics
- 1981
This paper summarizes some of the results we have recently obtained for a class of branching processes on a lattice with interactions (an extended version of this, containing additional results and…
First-passage percolation, network flows and electrical resistances
- Mathematics
- 1984
SummaryWe show that the first-passage times of first-passage percolation on ℤ2 are such that P(θ0nn(μ+ɛ)) decay geometrically as n→∞, where θ may represent any of the four usual first-passage-time…