Yuyang Feng

Email: yuyang at uchicago dot edu

I am a math Ph.D. student at UChicago from 2022, advised by Ewain Gwynne. I obtained my bachelor degree from from Peking University, where my advisor was Xinyi Li. Here is my CV (May, 2024).

My research interests lie in probability theory, especially in random planar map and Liouville quantum gravity theory. I also want to learn more about Yang-Mills theory and conformal field theory.

In a parallel universe, I might be a film director, a chef, or a dancer [1].

Research

Convergence of the loop-erased percolation explorer on UIHPT. In preparation.

We study critical site percolation on a uniform infinite half-planar triangulation with a white-black boundary condition. Previous studies have shown that the convergence of percolation interface-decorated maps to SLE_6-decorated \sqrt{8/3}-LQG surface under the local GHPU topology. In this work, we prove that the scaling limit of the loop-erasure of the percolation interface exists.

Triviality of critical Fortuin-Kasteleyn decorated planar maps for q > 4. To appear in Probability Theory and Related Fields. [arXiv] [Slides]

We consider infinite random planar maps decorated by the critical Fortuin-Kasteleyn model with parameter q>4. The paper demonstrates that when appropriately rescaled, these maps converge in law to the infinite continuum random tree as pointed metric-measure spaces, that is, with respect to the local Gromov-Hausdorff-Prokhorov topology. Furthermore, we also show that these maps do not admit any Fortuin-Kasteleyn loops with a macroscopic graph distance diameter. Our proof is based on Scott Sheffield's hamburger-cheeseburger bijection.

Graph distance exponents in mated-CRT maps (with Jinwoo Sung). Available upon request.

We construct the LQG metric on a class of quantum surfaces called (thin) quantum wedges, which are scale-invariant quantum surfaces formed by concatenation of beads. This is a generalization of the LQG metric defined in the complex plane. Furthermore, we give a Poissionian description of the distances between beads, which enables us to determine the phase transition of this metric: for a thin wedge with log singularity α where α ∈ (Q, Q + γ/2), the distance between two fixed beads is finite if and only if α ∈ (Q, Q + γ/dγ), where dγ is the Hausdorff dimension of γ-LQG surface.

As an application, we compute the exact value of graph distance exponents χ for mated-CRT maps G^ε, which are discretized matings of correlated continuum random trees and conjectured to converge in probability in the scaling limit with respect to the Gromov-Hausdorff-Prokhorov topology to LQG surface. Based on an assumption about the LQG metric in quantum wedges, the distance exponents are proven to be: