16 papers
Super-Brownian limits and the -point function for high-dimensional percolation
Arthur Blanc-Renaudie, Tom Hutchcroft
We prove that there exist positive constants and such that the high-dimensional critical percolation -point function is given by \[ T_{p_c}(x_1,x_2,\ldots,x_{k}) \sim V^…
A discontinuous percolation phase transition on the hierarchical lattice
Johannes Bäumler, Tom Hutchcroft
For long-range percolation on with translation-invariant edge kernel , it is a classical theorem of Aizenman and Newman (1986) that the phase transition is disconti…
Bounded-degree graphs of non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk
Tom Hutchcroft, Florentin Münch
We study the geometric properties of graphs with non-negative Ollivier-Ricci curvature, a discrete analogue of non-negative Ricci curvature in Riemannian geometry. We prove that fo…
Dimension dependence of critical phenomena in long-range percolation
Tom Hutchcroft
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of t…
Infinite stationary measures of co-compact group actions
Mohammedsaid Alhalimi, Tom Hutchcroft, Minghao Pan +2
Let be a finitely generated group, and let be a nondegenerate, finitely supported probability measure on . We show that every co-compact action on a locally comp…
Critical long-range percolation III: The upper critical dimension
Tom Hutchcroft
In long-range percolation on , points and are connected by an edge with probability , where is fixed and is a pa…