Romain Panis

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20242026

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math.PR2026

Mass scaling of the near-critical Ising model in dimensions $d \geq 4$

Romain Panis

We study the Ising model on $Z^{d}$ with $d \geq 4$ and derive near-critical bounds on the truncated two-point function $\langleσ_0;σ_x\rangle_{β,h} := \langleσ_0σ_x\rangle_{…

math.PR2026

On reversing the Simon-Lieb inequality in high-dimensional percolation

Romain Panis, Bruno Schapira

We study Bernoulli percolation on $Z^{d}$ in dimensions $d > 6$ . We prove that a classical consequence of the van den Berg-Kesten inequality, often referred to as the Simon-L…

math.PR2026

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 $Z^{d}$ ( $d > 2$ ) satisfying a short list of assumptions. The functions repr…

math.PR2026

Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation

Romain Panis, Bruno Schapira

We consider Bernoulli percolation on $Z^{d}$ with $d > 6$ . We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes pr…

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 $n$ (the one-arm probability) in several percolation models related to the Ising model. We…

math.PR2025

The incipient infinite cluster of the FK-Ising model in dimensions $d \geq 3$ and the susceptibility of the high-dimensional Ising model

Romain Panis

We consider the critical FK-Ising measure $I ¨ _{I^_{c}^{2}}$ on $Z^{d}$ with $d \geq 3$ . We construct the measure $Ï^\infty:=\lim_{|x|\rightarrow \infty}Ï_{Î²_c}[\:\cdot\: |\: 0\le…

Mass scaling of the near-critical Ising model in dimensions d≥4

On reversing the Simon-Lieb inequality in high-dimensional percolation

A random walk approach to high-dimensional critical phenomena

Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation

One-arm exponents of the high-dimensional Ising model

The incipient infinite cluster of the FK-Ising model in dimensions d≥3 and the susceptibility of the high-dimensional Ising model

Mass scaling of the near-critical Ising model in dimensions $d \geq 4$

The incipient infinite cluster of the FK-Ising model in dimensions $d \geq 3$ and the susceptibility of the high-dimensional Ising model