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arXiv · 2306.10625

Conformal invariance of random currents: a stability result

Hong-Bin Chen·Jiaming Xia
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Abstract

We show the convergence of the single sourceless critical random current to a limit identifiable with the nested CLE(3). Our approach is based on viewing the random current as a perturbation of the Ising interface, which is known to converge to CLE(3). Instead of focusing solely on the random current, we provide a general framework for the stability of scaling limits under the perturbation by superimposing an independent Bernoulli percolation.

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Hong-Bin Chen, Jiaming Xia. 2023-06-18. Conformal invariance of random currents: a stability result. https://arxiv.org/abs/2306.10625

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