Xin Sun's Homepage


About Me

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)

Publications and Preprints

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.

In Preparation

Phases of quantum Loewner evolution.
Ewain Gwynne, Jason Miller, Scott Sheffield and Xin Sun.

Invited Talks

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


Juhan Aru, Nathanael Berestycki, Ivan Corwin, Ewain Gwynne, Nina Holden, Yichao Huang, Gregory Lawler, Yiting Li, Dangzheng Liu, Asad Lodhia, Russell Lyons, Cheng Mao, Jason Miller, Yuval Peres, Scott Sheffield, Zhengdong Wang, Samuel Watson, Yichen Shen, David Wilson, Wei Wu.
The format for this webpage was stolen from Vinoth Nandakumar's webpage.