Research Interests

I study problems in probability theory and mathematical physics, employing techniques from applied analysis, probability, and combinatorics. My primary focus is on the mathematical structures underlying various random growth models in the Kardar-Parisi-Zhang universality class.

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)

  • A determinant identity for the sum of contour integral matrices, with Tejaswi Tripathi.

              arXiv:2604.24747, 2026.

  • Periodic KPZ fixed point with general initial conditions, with Jinho Baik and Yuchen Liao.

              arXiv:2603.01964, 2026.

  • Multipoint distributions of the KPZ fixed point with compactly supported initial conditions, 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, with Chen Ma and Tejaswi Tripathi.

              submitted, arXiv:2509.02524, 2025.

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

              submitted, arXiv:2507.20487, 2025.

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

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

  • Pinched-up periodic KPZ fixed point, 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, 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.

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

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

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

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

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

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

  • Multipoint distribution of TASEP

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

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

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

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

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

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

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

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

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

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

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

  • 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.

  • Discrete Toeplitz determinants and their applications

               PhD dissertation. May 2014.

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

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

  • 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.