Zijie Zhuang

activity

20232026

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5 papers · 1 filter

math.PR2025

Weak exponential metrics for high-dimensional log-correlated Gaussian fields

Andres A. Contreras Hip, Zijie Zhuang

For log-correlated Gaussian fields on $R^{d}$ with $d \geq 2$ , Ding-Gwynne-Zhuang (2023) established the existence of subsequential limits of exponential metrics obtained fr…

math.PR2025

Bounds on the distance exponent for higher-dimensional Liouville first passage percolation

Andres A. Contreras Hip, Zijie Zhuang

For $ξ \geq 0$ and $d \geq 3$ , the higher-dimensional Liouville first passage percolation (LFPP) is a random metric on $ε Z^{d}$ obtained by reweighting each vertex by $e^{ξh_…

math.PR2024

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.PR2024

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.PR2023

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\…