Research Interests

Grants/Funding

• 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 and publications (google scholar, arXiv)

• Multipoint distributions of the KPZ fixed point with compactly supported initial conditions (pdf), with Yuchen Liao.

              submitted, arXiv:2509.03246, 2025. 

• Limiting one-point fluctuations of the geodesic in the directed landscape near the endpoints when the geodesic length goes to infinity (pdf), with Chen Ma and Tejaswi Tripathi.

              submitted, arXiv:2509.02524, 2025.

• On the multipoint distribution formulas of the parabolic Airy process (pdf), with Aaron Ortiz.

              submitted, arXiv:2507.20487, 2025.

• An upper tail field of the KPZ fixed point (pdf), with Ray Zhang.

              Commun. Math. Phys., 406:198, 2025.

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

              Ann. Inst. H. Poincaré Probab. Statist., to appear, 2025+.

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

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

• When the geodesic becomes rigid in the directed landscape (pdf)

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

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

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

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

               Ann. Inst. H. Poincaré Probab. Statist., 58(1): 248-302, 2022.

• Periodic TASEP with general initial conditions (pdf), with Jinho Baik.

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

• Multipoint distribution of TASEP (pdf)

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

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

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

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

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

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

               Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 2, 1031-1057, 2018.

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

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

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

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

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

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

• Discrete Toeplitz determinants and their applications (pdf)

               PhD dissertation. May 2014.

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

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

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

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