Research

My research area is probability theory and mathematical physics. My recent research is focused on 2D random geometry and statistical physics, including SLE, Gaussian free field, random planar maps, Liouville quantum gravity and Liouville conformal field theory. I have also worked on uniform spanning trees and abelian sandpiles, as well as random matrices, fractional Gaussian fields and the Airy line ensemble.


Publications

Liouville dynamical percolation
Christophe Garban, Nina Holden, Avelio Sepúlveda and Xin Sun. Probability Theory and Related Fields, accepted. ArXiv.

Percolation on triangulations: a bijective path to Liouville quantum gravity
Olivier Bernardi, Nina Holden and Xin Sun. Memoirs of the AMS, accepted. ArXiv.

Natural parametrization of percolation interface and pivotal points
Nina Holden, Xinyi Li and Xin Sun. Annales de l’Institut Henri Poincaré, accepted. ArXiv.

Minkowski content of Brownian cut points
Nina Holden, Greg Lawler, Xinyi Li and Xin Sun. Annales de l’Institut Henri Poincaré, accepted. ArXiv.

Volume of metric balls in Liouville quantum gravity
Morris Ang, Hugo Falconet and Xin Sun. Electron. J. Probab., 25 (2020), no. 169, 50 pp. JournalArXiv.

Scaling limit of large triangulations of polygons
Marie Albenque, Nina Holden and Xin Sun. Electron. J. Probab., 25 (2020), no. 135, 43 pp. Journal. ArXiv.

Mating of trees for random planar maps and Liouville quantum gravity: a survey
Ewain Gwynne, Nina Holden and Xin Sun. Panoramas et Synthèses, accepted. ArXiv.

Weak LQG metrics and Liouville first passage percolation
Julien Dubédat, Hugo Falconet, Ewain Gwynne, Joshua Pfeffer and Xin Sun. Probability Theory and Related Fields, 178, 369–436(2020). Journal. ArXiv.

A mating-of-trees approach for graph distances in random planar maps
Ewain Gwynne, Nina Holden and Xin Sun. Probability Theory and Related Fields, 177, 1043–1102(2020). JournalArXiv.

Induced graphs of uniform spanning forests
Russell Lyons, Yuval Peres and Xin Sun. Annales de l’Institut Henri Poincaré, Vol. 56, No. 4 (2020), 2732-2744. Journal. ArXiv.

Occupation measure of random walks and wired spanning forests in balls of Cayley graphs
Russell Lyons, Yuval Peres, Xin Sun and Tianyi Zheng. Annales de la Faculté des Sciences de Toulouse, (2020) no. 1, pp. 97-109. Journal. ArXiv.

Four-dimensional loop-erased random walk
Gregory Lawler, Xin Sun and Wei Wu. Annals of Probability, Vol. 47, No. 6, 3866-3910 (2019). JournalArXiv.

A distance exponent for Liouville quantum gravity
Ewain Gwynne, Nina Holden and Xin Sun. Probability Theory and Related Fields, Vol. 173, Issue 3-4, 931-997 (2019). JournalArXiv.

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, Vol. 55, No. 1, 1-60 (2019). JournalArXiv.

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

SLE as a mating of trees in Euclidean geometry
Nina Holden and Xin Sun. Communications in Mathematical Physics. 364, 171-201 (2018). JournalArXiv.

Negative moments for Gaussian multiplicative chaos on fractal sets
Christophe Garban, Nina Holden, Avelio Sepúlveda and Xin Sun. Electron. Commun. Probab. 23 (2018), no. 100, 1-10. JournalArXiv.

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). JournalArXiv.

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). JournalArXiv.

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. JournalArXiv.

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). JournalArXiv.

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

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

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

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

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. JournalArXiv.

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). JournalArXiv.


Preprints

FZZ formula of boundary Liouville CFT via conformal welding
Morris Ang, Guillaume Remy and Xin Sun. ArXiv.

Integrability of SLE via conformal welding of random surfaces
Morris Ang, Nina Holden and Xin Sun. ArXiv.

Conformal welding of quantum disks
Morris Ang, Nina Holden and Xin Sun. ArXiv.

Probabilistic conformal blocks for Liouville CFT on the torus
Promit Ghosal, Guillaume Remy, Xin Sun and Yi Sun. ArXiv.

Convergence of uniform triangulations under the Cardy embedding
Nina Holden and Xin Sun. ArXiv.

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

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


Collaborators

Morris Ang, Juhan Aru, Marie AlbenqueNathanael BerestyckiOlivier BernardiIvan Corwin, Julien Dubédat, Hugo Falconet, Christophe GarbanEwain Gwynne, Promit Ghosal, Nina Holden, Yichao Huang, Gregory LawlerXinyi LiYiting Li, Dangzheng Liu, Asad Lodhia, Russell Lyons, Cheng Mao, Jason MillerYuval Peres, Joshua Pfeffer, Guillaume Remy Avelio Sepúlveda Scott SheffieldYichen ShenYi Sun, Zhengdong Wang, Samuel WatsonDavid WilsonWei WuTianyi Zheng.