Xinyi Li 李欣意

Assistant Professor at Beijing International Center for Mathematical Research, Peking University.

My main research interests are probability theory and statistical physics.

I was an L. E. Dickson instructor at the University of Chicago from 2016 to 2019. I received my Ph.D. from ETH Zurich. My advisor was Professor Alain-Sol Sznitman.

Contact Information

Address: Beijing International Center for Mathematical Research
Peking University
5 Yiheyuan Rd., Beijing 100871
China
地址: 100871北京市颐和园路5号北京大学北京国际数学研究中心
Office: 镜春园78号院(怀新园)75101-2
Coordinates: 39°59'47.4"N 116°18'36.0"E
E-mail: firstnamelastname at bicmr dot pku dot edu dot cn

A (not always up-to-date) version of my CV can be found here.

Seminars

I organize or co-organize the following seminars:

北京大学概率论系列报告 (The Probability Seminar at the School of Mathematical Sciences of PKU).
THU-PKU-BNU Joint Probability Webinar.
Probability seminars and mini-courses at BICMR.

Some ecordings of THU-PKU-BNU Joint Probability Webinar and probability events at BICMR are available at BICMR_proba@bilibili.

Student Seminars

I also organize or co-organize student seminars on various topics in current probability research. The theme varies every semester. Please contact me directly if you are interested.

Student Seminar on loop soups and related topics (Spring 2022).
3+X Seminar on triviality of high-dimensional Ising and Phi^4 models and Wulff crystals. (Spring 2022).
Student seminar (Fall 2021).
3+X Seminar (journal club) (Fall 2021).
Student Seminar on Gaussian free field, Liouville quantum gravity and Gaussian multiplicative chaos (Spring 2021).
Undergraduate and Graduate Journal club (Spring 2021).
3+X Seminar on random trees, random planar maps and their scaling limits (Autumn 2020).
Student Seminar on Schramm-Loewner Evolution (Autumn 2020).

Works

Y. Gao, X. Li, R. Liu and W. Qian. On the non-existence of several random fractals of zero dimension derived from Brownian motion. In preparation.
Y. Gao, X. Li, R. Liu, X. Liu and D. Shiraishi. Convergence of the frontier of planar random walk in natural parametrization. In preparation.
X. Li, Y. Liu and Y. Wang. Sharp asymptotics of disconnection time of large cylinders by simple and biased random walk. In preparation.
G. Cai, X. Li, D. Shiraishi and A. Xia. The boosted loop-erased random walk: scaling limit, phase transitions and space-filling property. In preparation.
C. Hao, X. Li, I. Okada and Y. Zheng. Favorite sites for simple random walk in two and more dimensions. Preprint, available at arXiv:2409.00995, 46 pages, 3 figures.
S. Hernandez-Torres, X. Li and D. Shiraishi. Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk. Preprint, available at arXiv:2403.07256, 50 pages.
Y. Gao, P. Panov, X. Li and D. Shiraishi. The scaling limit of the occupation measure of random walk cut points. Preprint, available at arXiv:2310.09592, 57 pages, 12 figures.
Y. Chang, H. Du and X. Li. Percolation threshold for metric graph loop soup. Bernoulli, 30, 4, pp. 3324-3333. Also available at arXiv:2304.08225.
H. Du, Y. Gao, X. Li and Z. Zhuang. Sharp estimates for probabilities of arm events in critical planar percolation. Comm. Math. Phys., 405, 182 (2024). Also available at arXiv:2205.15901.
X. Li and Z. Zhuang. On large deviations and intersection of random interlacements. Bernoulli, 30, 3, pp. 2102-2126 (2024). Also available at arXiv:2205.13953.
Y. Gao, X. Li and W. Qian. Multiple points on the boundaries of Brownian loop-soup clusters. Preprint, available at arXiv:2205.11468, 55 pages, 12 figures. Submitted.
X. Li and R. Liu. The intermediate level-sets of the four-dimensional membrane model. Preprint, available at arXiv:2205.03621, 22 pages. Submitted.
G. Cai and X. Li. On natural measures of SLE- and CLE-related random fractals. To appear in Ann. Inst. H. Poincaré Probab. Stat. Also available at arXiv:2205.01584.
X. Li and Y. Liu. Sharpness of phase transition for Voronoi percolation in hyperbolic space. Preprint, available at arXiv:2111.07276, 11 pages.
X. Li and D. Shiraishi. The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk. Electron. J. Probab., 19, 27, pp. 1-37 (2022).
X. Li and D. Shiraishi. Natural parametrization for the scaling limit of loop-erased random walk in three dimensions. Preprint, available at arXiv:1811.11685, 90 pages, 19 figures. Submitted.
N. Holden, X. Li and X. Sun. Natural parametrization of percolation interface and pivotal points. Ann. Inst. H. Poincaré Probab. Stat., 58, 1, pp. 7-25 (2022). Also available at arXiv:1804.07286.
N. Holden, G. Lawler, X. Li and X. Sun. Minkowski content of Brownian cut points. Ann. Inst. H. Poincaré Probab. Stat., 58, 1, pp. 455-488 (2022). Also available at arXiv:1803.10613.
X. Li and D. Shiraishi. One-point function estimates for loop-erased random walk in three dimensions. Electron. J. Probab., 24, 111, pp. 1-46 (2019).
M. Hilario, X. Li and P. Panov. Shape theorem and surface fluctuation for Poisson cylinders. Electron. J. Probab., 24, 68, pp. 1-16 (2019).
X. Li. Percolative properties of Brownian interlacements and its vacant set. J. Theor. Probab. 33, pp.1855–1893 (2020). Also available at arXiv:1610.08204.
X. Li. A lower bound for disconnection by simple random walk. Ann. Probab., 45, 2, pp. 879-931 (2017).
X. Li and A.-S. Sznitman. A lower bound for disconnection by random interlacements. Electron. J. Probab., 19, 17, pp. 1-26 (2014).
X. Li and A.-S. Sznitman. Large deviations for occupation time profiles of random interlacements. Probab. Theory Relat. Fields, 161, 1-2, pp. 309-350 (2015).

Teaching

Probability and Statistics (Spring 2022).
Advanced probability theory (Autumn 2021).
Probability and Statistics (Spring 2021, for Yuanpei College).
Advanced probability theory (Autumn 2020).
Selected Topics in Stochastic Processes (II) (Spring 2020).
Random Matrices surrogate (Autumn 2019.)