Jian Ding

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math.PR2026

Percolation of thick points of the log-correlated Gaussian field in high dimensions

Jian Ding, Ewain Gwynne, Zijie Zhuang

We prove that the set of thick points of the log-correlated Gaussian field contains an unbounded path in sufficiently high dimensions. This contrasts with the two-dimensional case,…

math.PR2025

Dynamical random field Ising model at zero temperature

Jian Ding, Peng Yang, Zijie Zhuang

In this paper, we study the evolution of the zero-temperature random field Ising model as the mean of the external field $M$ increases from $- \infty$ to $\infty$ . We focus on two t…

math.PR2025

Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension

Jian Ding, Ewain Gwynne, Zijie Zhuang

We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on $R^{d}$ for arbitrary $d \geq 2$ . More precisely, let $\{h_n\…