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- Corpus ID: 270062638

@inproceedings{Drewitz2024CriticalOP, title={Critical one-arm probability for the metric Gaussian free field in low dimensions}, author={Alexander Drewitz and Alexis Pr'evost and Pierre-Franccois Rodriguez}, year={2024}, url={https://api.semanticscholar.org/CorpusID:270062638}}

- Alexander Drewitz, Alexis Pr'evost, Pierre-Franccois Rodriguez
- Published 27 May 2024
- Physics, Mathematics

We investigate the bond percolation model on transient weighted graphs ${G}$ induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case $0<\nu<\frac{\alpha}{2}$, where $\alpha$ governs the polynomial volume growth of $G$ and $\nu$ the decay rate of the Green's function on…

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## 22 References

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Physics

It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops ("loop soup") of parameter one-half associated to a transient symmetric Markov jump process on a network is half…

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- Highly Influential[PDF]

- Alexander DrewitzAlexis Pr'evostPierre-Franccois Rodriguez
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Mathematics, Physics

We investigate the bond percolation model on transient weighted graphs ${G}$ induced by the excursion sets of the Gaussian free field on the corresponding metric graph. We assume that balls in ${G}$…

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- Highly Influential[PDF]

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Physics

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For massless vertex-transitive transient graphs, the percolation phase transition for the level sets of the Gaussian free field on the associated continuous cable system is particularly well…

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- Alexander DrewitzAlexis PrévostPierre-François Rodriguez
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Physics, Mathematics

Inventiones mathematicae

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this…

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- Highly Influential[PDF]

- Alexander DrewitzAlexis PrévostPierre-François Rodriguez
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Mathematics

Probability Theory and Related Fields

We investigate level sets of the Gaussian free field on continuous transient metric graphs G~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

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- Alexander DrewitzAlexis PrévostPierre-François Rodriguez
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Mathematics

For a large class of amenable transient weighted graphs $G$, we prove that the sign clusters of the Gaussian free field on $G$ fall into a regime of strong supercriticality, in which two infinite…

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- Alexis Prévost
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Mathematics, Physics

The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is…

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Mathematics, Physics

The Annals of Probability

We consider the Gaussian free field φ on Z, for d ≥ 3, and give sharp bounds on the probability that the radius of a finite cluster in the excursion set {φ ≥ h} exceeds a large value N for any height…

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This work studies level-set percolation for Gaussian free fields on metric graphs and gives an upper bound on the chemical distance between the two boundaries of a macroscopic annulus.

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