Romain Panis

activity

20222026

most citedTriviality of the scaling limits of critical Ising and

φ^{4}

models with effective dimension at least four

1 citations · 2 across the 18 of their papers we have counts for

collaborators

19 papers

cs.CV2026

Player-1: Learning to Play from Synthetic Experience

Mingyu Ouyang, Yiran Wang, Siyuan Hu +9

Computer-use agents have demonstrated strong capabilities in interpreting screens and executing keyboard and mouse actions. However, games, with their visually rich worlds and dive…

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

Supercritical sharpness for the random cluster representation of real-valued spin models

Trishen S. Gunaratnam, Dmitry Krachun, Christoforos Panagiotis +2

We study the supercritical regime $β > β_{c}$ of a large family of real-valued spin models on $Z^{d}$ , including the Blume-Capel and $P (φ)$ models. We consider their random clust…

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.PR2025

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 high-dimensional percolation revisited

Diederik van Engelenburg, Christophe Garban, Romain Panis +1

We consider sufficiently spread-out Bernoulli percolation in dimensions $d > 6$ . We present a short and simple proof of the up-to-constants estimate for the one-arm probability in…

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 supercritical phase of the $φ^{4}$ model is well behaved

Trishen S. Gunaratnam, Christoforos Panagiotis, Romain Panis +1

In this article, we analyse the $φ^{4}$ model on $Z^{d}$ in the supercritical regime $β > β_{c}$ . We consider a random cluster representation of the $φ^{4}$ model, which corresponds…

math.PR2024

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d > 4$

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 $d > 4$ . Among other results, we obtain up-to-constant estimate…

math.PR2024

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d > 6$

Hugo Duminil-Copin, Romain Panis

This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d > 6$ . We obtain an upper bound for the full-space…

math.PR2024

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 $ϕ_{β_{c}}$ on $Z^{d}$ with $d \geq 3$ . We construct the measure $ϕ^\infty:=\lim_{|x|\rightarrow \infty}ϕ_{β_c}[\:\cdot\: |\: 0\leftrig…

math-ph2024

The torus plateau for the high-dimensional Ising model

Yucheng Liu, Romain Panis, Gordon Slade

We consider the Ising model on a $d$ -dimensional discrete torus of volume $r^{d}$ , in dimensions $d > 4$ and for large $r$ , in the vicinity of the infinite-volume critical point $β_{c}$ .…

math.PR2024

New lower bounds for the (near) critical Ising and $φ^{4}$ models' two-point functions

Hugo Duminil-Copin, Romain Panis

We study the nearest-neighbour Ising and $φ^{4}$ models on $Z^{d}$ with $d \geq 3$ and obtain new lower bounds on their two-point functions at (and near) criticality. Together w…

math.PR2023

Exact cube-root fluctuations in an area-constrained random walk model

Lucas D'Alimonte, Romain Panis

This article is devoted to the study of the behaviour of a (1+1)-dimensional model of random walk conditioned to enclose an area of order $N^{2}$ . Such a conditioning enforces a glob…

math.PR2023

Scaling limit of the cluster size distribution for the random current measure on the complete graph

Dmitrii Krachun, Christoforos Panagiotis, Romain Panis

We study the percolation configuration arising from the random current representation of the near-critical Ising model on the complete graph. We compute the scaling limit of the cl…

math.PR2023★ 1 cited

Triviality of the scaling limits of critical Ising and $φ^{4}$ models with effective dimension at least four

Romain Panis

We prove that any scaling limit of a critical reflection positive Ising or $φ^{4}$ model of effective dimension $d_{eff}$ at least four is Gaussian. This extends the recent br…

math.PR2023

Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models

Trishen S. Gunaratnam, Romain Panis

We study corrections to the scaling limit of subcritical long-range Ising models with (super)-summable interactions on $Z^{d}$ . For a wide class of models, the scaling limit…

math.PR2022★ 1 cited

Random tangled currents for $φ^{4}$ : translation invariant Gibbs measures and continuity of the phase transition

Trishen S. Gunaratnam, Christoforos Panagiotis, Romain Panis +1

We prove that the set of automorphism invariant Gibbs measures for the $φ^{4}$ model on graphs of polynomial growth has at most two extremal measures at all values of $β$ . We also gi…

Player-1: Learning to Play from Synthetic Experience

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

Supercritical sharpness for the random cluster representation of real-valued spin models

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 high-dimensional percolation revisited

One-arm exponents of the high-dimensional Ising model

The supercritical phase of the φ4 model is well behaved

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions d>4

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions d>6

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

The torus plateau for the high-dimensional Ising model

New lower bounds for the (near) critical Ising and φ4 models' two-point functions

Exact cube-root fluctuations in an area-constrained random walk model

Scaling limit of the cluster size distribution for the random current measure on the complete graph

Triviality of the scaling limits of critical Ising and φ4 models with effective dimension at least four

Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models

Random tangled currents for φ4: translation invariant Gibbs measures and continuity of the phase transition

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

The supercritical phase of the $φ^{4}$ model is well behaved

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d > 4$

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d > 6$

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

New lower bounds for the (near) critical Ising and $φ^{4}$ models' two-point functions

Triviality of the scaling limits of critical Ising and $φ^{4}$ models with effective dimension at least four

Random tangled currents for $φ^{4}$ : translation invariant Gibbs measures and continuity of the phase transition