Yi Tian
I am Yi Tian, a PhD student in mathematics at the University of Cambridge (since 2024) advised by Jason Miller. I completed my master's at Universität Bonn in 2024 with Eveliina Peltola, and my undergraduate studies at Peking University in 2022 with Zhiyu Tian. Here is my CV.
My research interests are broadly in probability and statistical physics, and currently focus on conformal loop ensembles and Liouville quantum gravity.
Email: CRSid@cam.ac.uk
CRSid: yt425
Papers
Conformal loop ensembles
- Existence and uniqueness of the conformally invariant geodesic metric on conformal loop ensembles of central charge one (with E. Kammerer, K. Kavvadias, J. Miller, and W. Werner). In preparation.
- Existence and uniqueness of the Brownian motion on simple conformal loop ensemble carpets (with J. Miller). In preparation.
- Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets (with J. Miller). arXiv:2511.16208
Talks
- The conformally covariant geodesic metric on simple conformal loop ensemble carpets. Combinatorial and hyperbolic random planar geometry (CIRM Aug 2025).
- The conformally covariant geodesic metric on simple conformal loop ensemble carpets. Probabilistic methods in quantum field theory (Bonn Jul 2025).
Images
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Simulation of metric balls for the conformally covariant geodesic metric on CLE(\(\kappa\)) carpets with \(\kappa = 2.72, 2.85, 3, 10/3, 3.99\), respectively. Based on the work [GeoCLECarp].