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The asymptotic shape, large deviations and dynamical stability in first-passage percolation on cones
The asymptotic shape dynamical stability cones Probability
2011/9/2
Abstract: In this paper we consider first-passage percolation on certain subgraphs of the $\Z^d$ nearest neighbour graph. We present a three-fold extension of the Shape Theorem. Firstly, we show that ...
Asymptotics of first-passage percolation on 1-dimensional graphs
Asymptotics of first-passage percolation 1-dimensional graphs Probability
2011/9/2
Abstract: In this paper we consider standard first-passage percolation on certain 1-dimensional periodic graphs. One such graph of particular interest is the $\Z\times\{0,1,...,K-1\}^{d-1}$ nearest ne...
Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
Examples of non-polygonal infinite coexistence spatial growth models
2010/12/6
We construct an edge-weight distribution for i.i.d. first-passage percolation on Z2 whose limit shape is not a polygon and has extreme points which are arbitrarily dense in the boundary. Consequently,...
On the Non-Convexity of the Time Constant in First-Passage Percolation
First-passage percolation timeconstant convexity
2009/5/11
We give a counterexample to a conjecture of Hammersley and Welsh (1965) about the convexity of the time constant in first-passage percolation, as a functional on the space of distribution functions. T...