13 papers
On reversing the Simon-Lieb inequality in high-dimensional percolation
Romain Panis, Bruno Schapira
We study Bernoulli percolation on in dimensions . We prove that a classical consequence of the van den Berg-Kesten inequality, often referred to as the Simon-L…
A random walk approach to high-dimensional critical phenomena
Hugo Duminil-Copin, Aman Markar, Romain Panis +1
We present a "black box" proof of mean-field near-critical behaviour for a family of functions on () satisfying a short list of assumptions. The functions repr…
Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation
Romain Panis, Bruno Schapira
We consider Bernoulli percolation on with . We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes pr…
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…
The incipient infinite cluster of the FK-Ising model in dimensions and the susceptibility of the high-dimensional Ising model
Romain Panis
We consider the critical FK-Ising measure on with . We construct the measure $Ï^\infty:=\lim_{|x|\rightarrow \infty}Ï_{β_c}[\:\cdot\: |\: 0\le…
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…