Author

Arthur Blanc-Renaudie

Tel Aviv University

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Preprint Sep 2026

Markovian renormalisation for percolation in high-dimension: Semi-decidability of mean field behavior

We develop a new approach to study Bernoulli percolation in dimensions $d>6$. The key idea is to approximate open paths at probability $p'>p$ by a Markov chain of pointed $p$-open clusters. This allows us to transfer sharp information on the two point function from $p$ to $p'$. This inductively gives good asymptotic es...

Arthur Blanc-Renaudie · 0 citations

Preprint Jul 2026

Super-Brownian limits and the $k$-point function for high-dimensional percolation

We prove that there exist positive constants $A$ and $V$ such that the high-dimensional critical percolation $k$-point function is given by \[ T_{p_c}(x_1,x_2,\ldots,x_{k}) \sim V^{k-2} A^{2k-3} \sum_{T\in \mathsf{Tr}(k)} \sum_{\substack{\Phi:V(T)\to \mathbb{Z}^d \\ \Phi(i)=x_i \forall 1\leq i \leq k}} \prod_{\substack...

Arthur Blanc-Renaudie, Tom Hutchcroft · 0 citations