Tom Hutchcroft

activity

20162026

most citedThe critical two-point function for long-range percolation on the hierarchical lattice

5 citations · 6 across the 21 of their papers we have counts for

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Showing 2017Show all

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math.PR2017

Counterexamples for percolation on unimodular random graphs

Omer Angel, Tom Hutchcroft

We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with $p_{c} = p_{u}$ for Bernoulli bond percolation, as well as an example of a bounded degree, u…

math.PR2017

The Hammersley-Welsh bound for self-avoiding walk revisited

Tom Hutchcroft

The Hammersley-Welsh bound (1962) states that the number $c_{n}$ of length $n$ self-avoiding walks on $Z^{d}$ satisfies \[ c_n \leq \exp \left[ O(n^{1/2}) \right] μ_c^n, \] wh…