N. Beaton

activity

20102026

most citedTwo-dimensional self-avoiding walks and polymer adsorption: Critical fugacity estimates

38 citations · 218 across the 29 of their papers we have counts for

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3 papers · 1 filter

math.PR2024

Chemical distance for the half-orthant model

Nicholas Beaton, Mark Holmes, Xin Huang

The half-orthant model is a partially oriented model of a random medium involving a parameter $p \in [0, 1]$ , for which there is a critical value $p_{c} (d)$ (depending on the dimension…

math.PR2022★ 4 cited

The mean square displacement of random walk on the Manhattan lattice

Nicholas R. Beaton, Mark Holmes

We give an explicit formula for the mean square displacement of the random walk on the $d$ -dimensional Manhattan lattice after $n$ steps, for all $n$ and all dimensions $d \geq 2$ .

math.PR2019★ 3 cited

Alignment percolation

Nicholas R. Beaton, Geoffrey R. Grimmett, Mark Holmes

The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \geq 2$ dimensions. Salient features of the phase diagram are e…