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• W1629366105 abstract "We consider a model of long-range first-passage percolation on the $d$ dimensional square lattice $Z^d$ in which any two distinct vertices $x, y in Z^d$ are connected by an edge having exponentially distributed passage time with mean $||x-y||^{alpha+o(1)}$, where $alpha>0$ is a fixed parameter and $||cdot||$ is the $ell_1$-norm on $Z^d$. We analyze the asymptotic growth rate of the set $B_t$, which consists of all $x in Z^d$ such that the first-passage time between the origin 0 and $x$ is at most $t$, as $ttoinfty$. We show that depending on the values of $alpha$ there are four growth regimes: (i) instantaneous growth for $alpha<d$, (ii) stretched exponential growth for $alphain (d,2d)$, (iii) superlinear growth for $alphain (2d,2d+1)$ and finally (iv) linear growth for $alpha>2d+1$ like the nearest-neighbor first-passage percolation model corresponding to $alpha=infty$." @default.
• W1629366105 created "2016-06-24" @default.
• W1629366105 creator A5006605137 @default.
• W1629366105 creator A5043520324 @default.
• W1629366105 date "2013-09-23" @default.
• W1629366105 modified "2023-09-23" @default.
• W1629366105 title "Multiple phase transitions in long-range first-passage percolation on square lattices" @default.
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• W1629366105 hasPublicationYear "2013" @default.
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