7 papers · 1 filter
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 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…
The supercritical phase of the model is well behaved
Trishen S. Gunaratnam, Christoforos Panagiotis, Romain Panis +1
In this article, we analyse the model on in the supercritical regime . We consider a random cluster representation of the model, which corresponds…
An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions . Among other results, we obtain up-to-constant estimate…
An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions . We obtain an upper bound for the full-space…