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.


Selected Publications

Backbone exponent for two-dimensional percolation
Pierre Nolin, Wei Qian, Xin Sun, and Zijie Zhuang. (2023) ArXiv.

The moduli of annuli in random conformal geometry  
Morris Ang, Guillaume Remy and Xin Sun. (2022) ArXiv.

Integrability of the conformal loop ensemble
Morris Ang and Xin Sun. (2021) ArXiv.

FZZ formula of boundary Liouville CFT via conformal welding
Morris Ang, Guillaume Remy and Xin Sun. Journal of the European Mathematical Society, accepted. ArXiv.

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

Integrability of SLE via conformal welding of random surfaces
Morris Ang, Nina Holden and Xin Sun. Communications on Pure and Applied Mathematics, 2023. Journal. ArXiv.

Percolation on triangulations: a bijective path to Liouville quantum gravity
Olivier Bernardi, Nina Holden and Xin Sun. Memoirs of the AMS, 2023. Journal. ArXiv.

Convergence of uniform triangulations under the Cardy embedding
Nina Holden and Xin Sun. ACTA Mathematica, Vol. 230, No. 6, 93-203 (2023). 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.

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


Survey Articles

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.

Random planar geometry through the lens of uniform spanning tree.
Xin Sun. Bernoulli News, 26(2):10–13, 2019. Journal.

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


Full Publication List

Bootstrap, Markov Chain Monte Carlo, and LP/SDP hierarchy for the lattice Ising model
Minjae Cho and Xin Sun. Journal of High Energy Physics, (2023) Link.

Conformal welding of quantum disks and multiple SLE: the non-simple case
Morris Ang, Nina Holden, Xin Sun, and Pu Yu. (2023) ArXiv.

SLE partition functions via conformal welding of random surfaces  
Xin Sun and Pu Yu. (2023) ArXiv.

Backbone exponent for two-dimensional percolation
Pierre Nolin, Wei Qian, Xin Sun, and Zijie Zhuang. (2023) ArXiv.

Derivation of all structure constants for boundary Liouville CFT
Morris Ang, Guillaume Remy, Xin Sun, and Tunan Zhu. (2023) ArXiv.

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

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

FZZ formula of boundary Liouville CFT via conformal welding
Morris Ang, Guillaume Remy and Xin Sun. Journal of the European Mathematical Society, accepted. ArXiv.

Integrability of SLE via conformal welding of random surfaces
Morris Ang, Nina Holden and Xin Sun. Communications on Pure and Applied Mathematics, 2023. Journal. ArXiv.

Percolation on triangulations: a bijective path to Liouville quantum gravity
Olivier Bernardi, Nina Holden and Xin Sun. Memoirs of the AMS, 2023. Journal. ArXiv.

Mating of trees for random planar maps and Liouville quantum gravity: a survey
Ewain Gwynne, Nina Holden and Xin Sun. contribution to Topics in Statistical Mechanics, Panoramas et Synthèses, 2023. ArXiv.

Convergence of uniform triangulations under the Cardy embedding
Nina Holden and Xin Sun. ACTA Mathematica, Vol. 230, No. 6, 93-203 (2023). Journal. ArXiv.

Baxter permuton and Liouville quantum gravity  
Jacopo Borga, Nina Holden, Xin Sun and Pu Yu. Probability Theory and Related Fields, (2023). Journal. ArXiv.

The SLE loop via conformal welding of quantum disks
Morris Ang, Nina Holden and Xin Sun. Electron. J. Probab., 28 (2023). Journal. ArXiv.

Conformal welding of quantum disks
Morris Ang, Nina Holden and Xin Sun. Electron. J. Probab., 28 (2023). Journal. ArXiv.

Equivalence of Liouville measure and Gaussian free field
Nathanael Berestycki, Scott Sheffield and Xin Sun. Annales de l’Institut Henri Poincaré, 2023, Vol. 59, No. 2, 795–816. Journal. ArXiv.

Brownian half-plane excursion and critical Liouville quantum gravity
Juhan Aru, Nina Holden, Ellen Powell and Xin Sun. Journal of the London Mathematical Society, (2022). JournalArXiv.

Natural parametrization of percolation interface and pivotal points
Nina Holden, Xinyi Li and Xin Sun. Annales de l’Institut Henri Poincaré, Vol. 58, No. 1 (2022). ArXiv.

Minkowski content of Brownian cut points
Nina Holden, Greg Lawler, Xinyi Li and Xin Sun. Annales de l’Institut Henri Poincaré, Vol. 58, No. 1 (2022). ArXiv.

Quantum triangles and imaginary geometry flow lines
Morris Ang, Xin Sun, and Pu Yu. (2022) ArXiv.

Permutons, meanders, and SLE-decorated Liouville quantum gravity
Jacopo Borga, Ewain Gwynne, and Xin Sun. (2022) ArXiv.

The moduli of annuli in random conformal geometry  
Morris Ang, Guillaume Remy and Xin Sun. (2022) ArXiv.

Liouville dynamical percolation
Christophe Garban, Nina Holden, Avelio Sepúlveda and Xin Sun. Probability Theory and Related Fields, (2021). Journal. ArXiv.

Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense
Ewain Gwynne, Nina Holden and Xin Sun. Electron. J. Probab., 26 (2021), 58pp. Journal. ArXiv.

Integrability of the conformal loop ensemble
Morris Ang and Xin Sun. (2021)  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.

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.

Random planar geometry through the lens of uniform spanning tree.
Xin Sun. Bernoulli News, 26(2):10–13, 2019. Journal.

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.

Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden and Xin Sun. (2016) ArXiv.

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

Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map III: finite volume case
Ewain Gwynne and Xin Sun. (2015) ArXiv.

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

Uniform spanning forest and the bi-Laplacian Gaussian field
Xin Sun and Wei Wu. (2013) 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. 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.


Collaborators

Morris Ang, Juhan Aru, Marie AlbenqueNathanael BerestyckiOlivier Bernardi, Jacopo BorgaIvan 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 Wu, Pu Yu, Tianyi Zheng, Tunan Zhu.