3 papers
math.PR2026
The impact of disorder and non-convex interactions on delocalisation of height functions
Paul Dario, Diederik van Engelenburg, Christophe Garban
We study the behaviour of four spins systems (the XY model, the Villain model, the XY height function and the integer-valued Gaussian free field) in the presence of a non-elliptic…
math.PR2025
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…
math.PR2025
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…