Xin Sun's Homepage

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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 is supported by NSF Award DMS-1811092.

Research

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.

CV

(Last updated: November 27, 2017)

Publications

A distance exponent for Liouville quantum gravity
Ewain Gwynne, Nina Holden and Xin Sun. Probability Theory and Related Fields. Journal. ArXiv.

SLE as a mating of trees in Euclidean geometry
Nina Holden and Xin Sun. Communications in Mathematical Physics, Journal. ArXiv.

Occupation measure of random walks and wired spanning forests in balls of Cayley graphs
Russell Lyons, Yuval Peres and Xin Sun. Annales de la Faculté des Sciences de Toulouse, accepted. ArXiv.

Almost sure multifractal spectrum of SLE
Ewain Gwynne, Jason Miller and Xin Sun. Duke Math. J., Vol. 167, No. 6, 1099-1237 (2018). Journal. ArXiv.

Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times
Ewain Gwynne, Cheng Mao and Xin Sun. Annales de l'Institut Henri Poincaré, to appear. ArXiv.

Brownian motion correlation in the peanosphere for $\kappa> 8$
Ewain Gwynne, Nina Holden, Jason Miller and Xin Sun. Annales de l'Institut Henri Poincaré, Vol. 53, No. 4, 1866-1889 (2017). Journal. ArXiv.

Two perspectives of the unit area quantum sphere and their equivalence
Juhan Aru, Yichao Huang and Xin Sun. Communications in Mathematical Physics. 356, 261-283 (2017). Journal. ArXiv.

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 Vol. 11, Issue 7, 441-446 (2017). Journal. ArXiv.

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. Journal. ArXiv.

Sandpiles and unicycles on random planar maps
David Wilson and Xin Sun. Electron. Commun. Probab. 21(2016), no. 57, 1-12. Journal. ArXiv.

Fractional Gaussian field: a survey
Asad Lodhia, Scott Sheffield, Xin Sun and Samuel Watson. Probability Surveys, Vol 13(2016), 1-56. Journal. ArXiv.

On fluctuations for random band Toeplitz matries
Yiting Li and Xin Sun. Random Matrices: Theory and Applications. Vol. 4, No.2(2015). Journal. ArXiv.

Ergodicity of the Airy line ensemble
Ivan Corwin and Xin Sun. Electron. Commun. Probab. 19(2014), no. 49, 1-11. Journal. ArXiv.

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. Journal. ArXiv.

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). Journal. ArXiv.

Preprints

Liouville dynamical percolation
Christophe Garban, Nina Holden, Avelio Sepúlveda and Xin Sun. preliminary version.

Negative moments for Gaussian multiplicative chaos on fractal sets
Christophe Garban, Nina Holden, Avelio Sepúlveda and Xin Sun. ArXiv.

Natural parametrization of percolation interface and pivotal points
Nina Holden, Xinyi Li and Xin Sun. ArXiv.

Minkowski content of Brownian cut points
Nina Holden, Greg Lawler, Xinyi Li and Xin Sun. ArXiv.

A mating-of-trees approach for graph distances in random planar maps
Ewain Gwynne, Nina Holden and Xin Sun. ArXiv.

Schnyder woods, SLE$_{16}$ and Liouville quantum gravity
Yiting Li, Xin Sun and Samuel Watson. ArXiv.

Loop-erased random walk, uniform spanning forests and bi-Laplacian Gaussian field in the critical dimension
Gregory Lawler, Xin Sun and Wei Wu. ArXiv.

Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden and Xin Sun. ArXiv.

Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map III: finite volume case
Ewain Gwynne and Xin Sun. ArXiv.

Equivalence of Liouville measure and Gaussian free field
Nathanael Berestycki, Scott Sheffield and Xin Sun. ArXiv.

Uniform spanning forest and the bi-Laplacian Gaussian field
Xin Sun and Wei Wu. ArXiv.

In Preparation

Uniform triangulation with simple boundary converges to the Brownian disk.
Marie Albenque, Xin Sun and Yuting Wen.

Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense.
Ewain Gwynne, Nina Holden and Xin Sun.

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

Collaborators

Marie Albenque, Juhan Aru, Nathanael Berestycki, Olivier Bernardi, Ivan Corwin, Christophe Garban, Ewain Gwynne, Nina Holden, Yichao Huang, Gregory Lawler, Xinyi Li, Yiting Li, Dangzheng Liu, Asad Lodhia, Russell Lyons, Cheng Mao, Jason Miller, Yuval Peres, Avelio Sepúlveda , Scott Sheffield, Yichen Shen, Zhengdong Wang, Samuel Watson, Yuting Wen, David Wilson, Wei Wu.