I am a Junior Fellow at Simons Society of Fellows, working at the Department of Mathematics at Columbia University. Before coming to Columbia, I got my Ph.D. degree in mathematics from MIT and my B.S. degree in mathematics from Peking University. My Ph.D. adviser is Scott Sheffield. In the summer of 2014, I was a research intern at Microsoft Research Theory Group , where I was mentored by David Wilson.

My research area is probability theory and mathematical physics. So far I have done research on random planar geometry, including SLE, Gaussian free field, random planar maps and Liouville quantum gravity. I have also worked on uniform spanning trees and abelian sandpiles, as well as random matrices, fractional Gaussian fields and the Airy line ensemble.

(Last updated: June 26, 2017)

**Schnyder woods, SLE$_{16}$ and Liouville quantum gravity**

Yiting Li, Xin Sun and Samuel Watson.
arxiv:1705.03573.

**Occupation measure of random walks and wired spanning forests in balls of Cayley graphs**

Russell Lyons, Yuval Peres and Xin Sun.
arxiv:1705.03576.

**SLE as a mating of trees in Euclidean geometry**

Nina Holden and Xin Sun.
arxiv:1610.05272.

**Deep Learning with Coherent Nanophotonic Circuits**

Yichen Shen, Nicholas C. Harris, Scott Skirlo, Mihika Prabhu, Tom Baehr-Jones, Micheal Hochberg, Xin Sun, Shijie Zhao, Hugo Larochelle, Dirk Englund and Marin Soljacic.
*Nature Photonics* (2017).
arxiv:1610.02365.

**Loop-erased random walk, uniform spanning forests and bi-Laplacian Gaussian field in the critical dimension**

Gregory Lawler, Xin Sun and Wei Wu.
arxiv:1608.02987.

**A distance exponent for Liouville quantum gravity**

Ewain Gwynne, Nina Holden and Xin Sun.
arxiv:1606.01214.

**Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense**

Ewain Gwynne, Nina Holden and Xin Sun.
arxiv:1603.01194.

**Two perspectives of the unit area quantum sphere and their equivalence**

Juhan Aru, Yichao Huang and Xin Sun.
*Communications in Mathematical Physics, to appear.*
arxiv:1512.06190.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map III: finite volume case**

Ewain Gwynne and Xin Sun.
arxiv:1510.06346.

**Brownian motion correlation in the peanosphere for $\kappa> 8$**

Ewain Gwynne, Nina Holden, Jason Miller and Xin Sun.
*Annales de l'Institut Henri Poincaré, to appear.*
arxiv:1510.04687.

**Sandpiles and unicycles on random planar maps**

David Wilson and Xin Sun.
*Electron. Commun. Probab.* 21(2016), no. 57, 1-12.
arxiv:1506.08881.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random
planar map II: local estimates and empty reduced word exponent**

Ewain Gwynne and Xin Sun.
*Electron. J. Probab.* 22(2017), no. 45, 1-56.
arxiv:1505.03375.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times**

Ewain Gwynne, Cheng Mao and Xin Sun.
arxiv:1502.00546.

**Almost sure multifractal spectrum of SLE**

Ewain Gwynne, Jason Miller and Xin Sun.
arxiv:1412.8764.

**On fluctuations for random band Toeplitz matries**

Yiting Li and Xin Sun.
*Random Matrices: Theory and Applications.* Vol. 4, No.2(2015).
arxiv:1412.5232.

**Equivalence of Liouville measure and Gaussian free field**

Nathanael Berestycki, Scott Sheffield and Xin Sun.
arxiv:1410.5407.

**Fractional Gaussian field: a survey**

Asad Lodhia, Scott Sheffield, Xin Sun and Samuel Watson. *Probability Surveys*, Vol 13(2016), 1-56.
arxiv:1407.5598.

**Ergodicity of the Airy line ensemble**

Ivan Corwin and Xin Sun. *Electron. Commun. Probab.* 19(2014), no. 49, 1-11.
arxiv:1405.0464.

**Uniform spanning forest and the bi-Laplacian Gaussian field**

Xin Sun and Wei Wu.
arxiv:1312.0059.

**Fluctuations of eigenvalues for random Toeplitz and related matrices**

Dangzheng Liu, Xin Sun and Zhengdong Wang.
*Electron. J. Probab.* 17(2012), no. 95, 1-22.
arxiv:1010.3394v2.

**A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth**

Yiting Li, Dangzheng Liu, Xin Sun and Zhengdong Wang.
*Statistics and Probability Letters* 08/2011; 81 (12).
arxiv:1108.2810.

**Phases of quantum Loewner evolution.**

Ewain Gwynne, Jason Miller, Scott Sheffield and Xin Sun.

**2017.03 Brandeis Every Topic Seminar**, Brandeis University

**2017.03 SLE, GFF and LQG in NYC**, Columbia University, New York, US

**2017.01 Stanford Probability Seminar**, Stanford University

**2016.12 Michigan State University Probability Seminar**, Michigan State University

**2016.11 Talks in theoretical sciences 2016**, ETH Zurich

**2016.11 UBC Probability Seminar**, University of British Columbia

**2016.10 NYU Probability and Mathematical Physics Seminar**, New York University

**2016.06 Workshop on Recent Developments in SLE**, Mittag-Leffler Institute, Stockholm, Sweden

**2016.04 Brown Discrete Math Seminar**, Brown University

**2016.04 Columbia Probability Seminar**, Columbia University

**2016.02 3rd Annual Graduate Student Math Conference in Analysis **, Brown University

**2015.11 Northwestern Analysis Seminar**, Northwestern University

**2015.11 Chicago Probability and Statistical Physics Seminar**, University of Chicago

**2015.11 MIT Probability Seminar**, MIT

**2015.09 Harvard Random Matrix and Probability Seminar **, Harvard University

**2015.07 Peking University Youth Probability Forum**, Peking University

**2015.05 Seymour Sherman Lecture and Conference**, Indiana University

**2015.01 Workshop on Conformally Invariant Scaling Limits**, Issac Newton Institute, Cambridge, UK