[PDF] Critical one-arm probability for the metric Gaussian free field in low dimensions | Semantic Scholar (2024)

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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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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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Arm exponent for the Gaussian free field on metric graphs in intermediate dimensions
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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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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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