{"ID":23551633,"CreatedAt":"2026-09-18T04:14:56.806955139Z","UpdatedAt":"2026-09-18T04:14:56.806955139Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20764","arxiv_id":"2609.20764","title":"Markovian renormalisation for percolation in high-dimension: Semi-decidability of mean field behavior","abstract":"We develop a new approach to study Bernoulli percolation in dimensions $d\u003e6$. The key idea is to approximate open paths at probability $p'\u003ep$ 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 estimates on the two point function as $p\\uparrow p_c$. As a main application, we show that having critical meanfield behavior is a semi-decidable problem. Along the way, we also prove sharp asymptotics for the susceptibility and the average radius of gyration, and prove a local central limit theorem for the slightly subcritical two-point function.","short_abstract":"We develop a new approach to study Bernoulli percolation in dimensions $d\u003e6$. The key idea is to approximate open paths at probability $p'\u003ep$ 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...","url_abs":"https://arxiv.org/abs/2609.20764","url_pdf":"https://arxiv.org/pdf/2609.20764v1","authors":"[\"Arthur Blanc-Renaudie\"]","published":"2026-09-17T17:44:19Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math-ph\"]","methods":"[]","has_code":false}