One-arm exponent of critical metric graph Gaussian free field in high dimensions

About the speaker

I am a PhD student at the School of Mathematical Science, Peking University. My supervisor is Prof. Yuan Zhang. Currently, my research interests include some stochastic models related to random walks, such as random interlacements, Gaussian free field, and diffusion-limited aggregation.

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 (IIC).