Research

My research mainly concerns a family of one-dimensional stochastic growth models known as the Kardar-Parisi-Zhang (KPZ) universality class, focusing on several perspectives on Gibbsian line ensembles, last passage percolation, and models with integrable or exactly solvable structure, including the asymmetric simple exclusion process and the stochastic six-vertex model.

Papers

1. The lower tail of \(q\)-pushTASEP.
   With Ivan Corwin.
   Comm. Math. Phys., 405, no. 3, 64 (2024).    arXiv.    Slides.
   
2. Brownian structure in the KPZ fixed point.
   With Jacob Calvert and Alan Hammond.
   Astérisque, vol. 441 (2023).    arXiv.    Slides.
   
3. Optimal tail exponents in general last passage percolation via bootstrapping & geodesic geometry.
   With Shirshendu Ganguly.
   Probab. Theory Relat. Fields, 186, no. 1–2, 221–284 (2023).    arXiv.    Slides.
   
4. Local and global comparisons of the Airy difference profile to Brownian local time.
   With Shirshendu Ganguly.
   Ann. Inst. H. Poincaré Probab. Statist., 59, no. 3, 1342--1374 (2023).    arXiv.    Slides.
   
5. Exceptional times when the KPZ fixed point violates Johansson's conjecture on maximizer uniqueness.
   With Ivan Corwin, Alan Hammond, and Konstantin Matetski.
   Electron. J. Probab., 28, no. 11, 1-81 (2023).    arXiv.    Slides.
   
6. Interlacing and scaling exponents for the geodesic watermelon in last passage percolation.
   With Riddhipratim Basu, Shirshendu Ganguly, and Alan Hammond.
   Comm. Math. Phys., 393, no. 3, 1241–1309 (2022).    arXiv.
   
7. Lower Deviations in \(\beta\)-ensembles and Law of Iterated Logarithm in Last Passage Percolation.
   With Riddhipratim Basu, Shirshendu Ganguly, and Manjunath Krishnapur.
   Israel J. Math., 242, no. 1, pages 291–324, (2021).    arXiv.
   
8. Critical point for infinite cycles in a random loop model on trees.
   With Alan Hammond.
   Ann. Appl. Probab., 29, no. 4, 2067–2088, (2019).    arXiv.    Slides.

Preprints

1. Scaling limit of the colored ASEP and stochastic six-vertex models.
   With Amol Aggarwal and Ivan Corwin.
   arXiv.    Slides.    Browser simulation.    Code for Julia simulations.
   
2. Brownian bridge limit of path measures in the upper tail of KPZ models.
   With Shirshendu Ganguly and Lingfu Zhang.
   arXiv.    Slides.
   
3. Sharp upper tail estimates and limit shapes for the KPZ equation via the tangent method.
   With Shirshendu Ganguly.
   arXiv.    Slides.
   

Expository writing

1. Fractal structure in the directed landscape.
   With Shirshendu Ganguly.
   For a special issue in honour of Rajeeva L. Karandikar. We plan on expanding this in the future.
   

Talks/Slides (same as above)

• Scaling limit of ASEP.
  
• Upper tail scaling limit of continuum path measures in KPZ.
  
• The lower tail of \(q\)-pushTASEP.
  
• Understanding the upper tail behaviour of the KPZ equation via the tangent method.
  
• The Airy difference profile and Brownian local time.
  
• Fractal dimension of multiple maximizers in the KPZ fixed point.
  
• Bootstrapping to optimal tail exponents in last passage percolation.
  
• Brownian structure in universal KPZ objects.
  
• A phase transition in a random loop model on infinite trees.
  

Thesis

Probabilistic and geometric methods in last passage percolation.