One-arm exponent of critical metric graph Gaussian free field in high dimensions
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Title: |
One-arm exponent of critical metric graph Gaussian free field in high dimensions |
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Speaker: |
蔡振豪 博士，北京大学 |
| Inviter: |
姚昌龙 副研究员 |
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Time & Venue: |
2023.12.1 15:00 N613 |
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Abstract: |
We prove that for the critical level-set of Gaussian free field on the metric graph generated by Z^d (d>6), the one-arm probability (i.e. the probability of the event that the origin is connected to the boundary of the box B(N)) is proportional to N^{-2}, where B(N) is centered at the origin and has side length 2N. This paper is a joint work with Prof. Jian Ding. In addition to presenting the proof idea, this talk will also involve some interesting open questions, including the one-arm exponent in low dimensions, the structure of large clusters, and the incipient infinite cluster. |
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