Hi! I am a fourth-year PhD student in Statistics at UPenn. My advisors are Jian Ding and Xin Sun.
I am interested in probability theory with focus on statistical mechanics and random geometry. In particular, I have worked on percolation theory, Schramm-Loewner evolution, log-correlated Gaussian fields, Liouville quantum gravity, and disordered spin models.
My email is zijie123 at wharton.upenn.edu. Here is my CV.
Percolation of thick points of the log-correlated Gaussian field in high dimensions
with Jian Ding and Ewain Gwynne. arXiv:2410.22075.
Dynamical random field Ising model at zero temperature
with Jian Ding and Peng Yang. arXiv:2410.20457.
The bulk one-arm exponent for the CLE percolations
with Haoyu Liu, Xin Sun and Pu Yu. arXiv:2410.12724.
Backbone exponent and annulus crossing probability for planar percolation
with Pierre Nolin, Wei Qian and Xin Sun. arXiv:2410.06419.
Annulus crossing formulae for critical planar percolation
with Xin Sun and Shengjing Xu. arXiv:2410.04767.
Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension
with Jian Ding and Ewain Gwynne. arXiv:2310.03996.
Backbone exponent for two-dimensional percolation
with Pierre Nolin, Wei Qian and Xin Sun. arXiv:2309.05050.
Reported in Quanta Magazine and Journal club for condensed matter physics.
Boundary touching probability and nested-path exponent for non-simple CLE
with Morris Ang, Xin Sun and Pu Yu. Annals of Probability (to appear). arXiv:2401.15904.
Sharp asymptotics for arm probabilities in critical planar percolation
with Hang Du, Yifan Gao and Xinyi Li. Communications in Mathematical Physics (2024). Journal.
On large deviations and intersection of random interlacements
with Xinyi Li. Bernoulli (2024). Journal.
Long range order for random field Ising and Potts models
with Jian Ding. Communications on Pure and Applied Mathematics (2024). Journal.
On the percolative properties of the intersection of two independent interlacements
ALEA (2021). Journal.
Coauthors: Morris Ang, Jian Ding, Hang Du, Yifan Gao, Ewain Gwynne, Xinyi Li, Haoyu Liu, Pierre Nolin, Wei Qian, Xin Sun, Shengjing Xu, Peng Yang, Pu Yu