I am Xiaochuan, research fellow at the University of Bath. My research interest lies in Probability Theory and its connection with geometric and topological data analysis, statistical physics, high dimensional statistics, multifractality, and number theory. Previously I held the Luxembourg-Singapore bilateral postdoc position, and visiting assistant professor position at Michigan State University. I wrote my PhD thesis at Université Paris-Est.
Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos.(with Subhroshekhar Ghosh, Krishna Balasubramanian).ICML 2020
Restricted hypercontractivity on the Poisson space.(with Ivan Nourdin, Giovanni Peccati).Proc. Amer. Math. Soc. 148 (2020), no. 8, 3617–3632.
Uniform dimension results for the inverse images of symmetric Lévy processes.(with Hyunchul Park, Yimin Xiao).J. Theoret. Probab. 33 (2020), no. 4, 2213–2232.
Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality.(with Ivan Nourdin, Giovanni Peccati). Electron. Commun. Probab. Volume 24 (2019), paper no. 34, 12 pp.
 On the favorite points of symmetric Lévy processes.(with Bo Li, Yimin Xiao). J. Theoret. Probab. 32(2019), No.4, 1943-1972
Multifractal properties of sample paths of ground state-transformed jump processes.(with Jozsef Lorinczi). Chaos Solitons Fractals 120 (2019) 83–94.
On sojourn of Brownian motion inside moving boundaries.(with Stéphane Seuret). Stochastic Process. Appl. 129 (2019) 978–994.
Uniform Hausdorff dimension result for the inverse images of stable Lévy processes(with Renming Song, Yimin Xiao). Electron. Commun. Probab., Volume 23 (2018), paper no. 75, 10 pp.
Multifractality of jump diffusion processes. Ann. Inst. Henri Poincaré Probab. Stat. 54 (2018), No.4, 2042-2074.
Hausdorff dimension of the range and the graph of stable-like processes. J. Theoret. Probab. 31 (2018), No.4, 2412-2431.
Multifractal analysis for the occupation measure of stable-like processes.(with Stéphane Seuret), Electron. J. Probab. 22 (2017), Paper No. 47, 36 pp.
Quantitative two-scale stabilization on the Poisson space.(with Raphaël Lachièze-Rey, Giovanni Peccati).
Multivariate normal approximation on the Wiener space: new bounds in the convex distance.(with Ivan Nourdin, Giovanni Peccati).
Non-integrable stable approximation by Stein’s method.(with Peng Chen, Ivan Nourdin, Lihu Xu and Rui Zhang).
Multivariate stable approximation in Wasserstein distance by Stein’s method.(with Peng Chen, Ivan Nourdin and Lihu Xu).