19 citations · 19 across the 6 of their papers we have counts for
6 papers
One-arm exponents of high-dimensional percolation revisited
Diederik van Engelenburg, Christophe Garban, Romain Panis +1
We consider sufficiently spread-out Bernoulli percolation in dimensions . We present a short and simple proof of the up-to-constants estimate for the one-arm probability in…
One-arm exponents of the high-dimensional Ising model
Diederik van Engelenburg, Christophe Garban, Romain Panis +1
We study the probability that the origin is connected to the boundary of the box of size (the one-arm probability) in several percolation models related to the Ising model. We…
On the duality between height functions and continuous spin models
Diederik van Engelenburg, Marcin Lis
We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use i…
The number of ends in the uniform spanning tree for recurrent unimodular random graphs
Diederik van Engelenburg, Tom Hutchcroft
We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together…
An elementary proof of phase transition in the planar XY model
Diederik van Engelenburg, Marcin Lis
Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by…
An upper bound on the two-arms exponent for critical percolation on
Jacob van den Berg, Diederik van Engelenburg
Consider critical site percolation on with . Cerf (2015) pointed out that from classical work by Aizenman, Kesten and Newman (1987) and Gandolfi, Grimmett…