Research Interests

I am working in probability and mathematical physics. I am interested in understanding the mathematical structures behind some random growth models, especially the universal limiting behaviors of these models after a long time.

Support

• KU Start up funding, $30,000, 2017-2021

• KU New Faculty Research Grant, $8,000, 2018-2021

• Simons Collaboration Grant No. 637861, $42,000 (only awarded $8,400 due to receiving the NSF grants), 2019-2024

• NSF DMS-1953687, $168,627, 2020-2024

• NSF DMS-2246683, $296,885, 2023-2026

• Department funding, $30,000, 2023-2026

• AIM’s SQuaREs program, 2024-2027

Preprints/publications (google scholar, arXiv)

• Pinched-up periodic KPZ fixed point, with Jinho Baik.

submitted. arXiv:2403.01624

• A conditional scaling limit of the KPZ fixed point with height tending to infinity at one location, with Yizao Wang.

Electron. J. Probab., 29: 1-27, 2024.

• When the geodesic becomes rigid in the directed landscape

• Electron. Commun. Probab., 27: 1-13, 2022. PDF.

• One-point distribution of the geodesic in directed last passage percolation

• Probab. Theory Related Fields, 184: 425-491, 2022. PDF.

• Limiting one-point distribution of periodic TASEP, with Jinho Baik and Guilherme Silva.

• Ann. Inst. H. Poincaré B, 58(1): 248-302, 2022. PDF.

• Periodic TASEP with general initial conditions, with Jinho Baik.

• Probab. Theory Related Fields, 179: 1047-1144, 2021. PDF.

• Multipoint distribution of TASEP

• Ann. Probab., Vol. 50, No. 4, 1255-1321, 2022. PDF.

• Integral formulas of ASEP and q-TAZRP on a ring, with Axel Saenz and Dong Wang.

• Commun. Math. Phys., 379: 261-325, 2020. PDF.

• Multi-point distribution of periodic TASEP, with Jinho Baik.

• J. Amer. Math. Soc., 32: 609-674, 2019. PDF.

• Height fluctuations of stationary TASEP on a ring in relaxation time scale

• Ann. Inst. H. Poincaré B, Volume 54, Number 2, 1031-1057, 2018. PDF.

• TASEP on a ring in sub-relaxation time scale, with Jinho Baik.

• J. Stat. Phys., 165: 1051-1085, 2016. PDF.

• Fluctuations of TASEP on a ring in relaxation time scale, with Jinho Baik.

• Comm. Pure Appl. Math., Vol. 71, Issue 4, 747-813, 2018. PDF.

• Fluctuations of TASEP and LPP with general initial data, with Ivan Corwin and Dong Wang.

• Ann. Appl. Probab., Vol. 26, Number 4, 2030-2082, 2016. PDF.

• Discrete Toeplitz determinants and their applications

• PhD dissertation. May 2014, PDF.

• On the average of the Airy process and its time reversal, with Jinho Baik.

• Electron. Commun. Probab., 18, no.89, 1-10, 2013. PDF.

• Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes, with Jinho Baik.

• Int. Math. Res. Not., Vol. 2014, Issue 20, 5737-5768, 2014. PDF.