150 N. University Street
West Lafayette, IN 47907

I am an Assistant Professor in the Department of Mathematics at Purdue University, specializing in probability. My research is currently mainly focused on the infinite volume structure of random walks in random potentials (RWRP). The RWRP model is connected to many interesting things happening in probability today and, in particular, to the Kardar-Parisi-Zhang universality class. I am also interested in related topics like stochastic partial differential equations and interacting particle systems.

Prior to coming to Purdue, I earned my Ph.D. in Mathematics in 2016 at the University of Wisconsin - Madison under the supervision of Benedek Valkó. I spent the 2016-2017 academic year as a postdoc in the Laboratoire de Probabilités et Modèles Aléatoires at Université Paris Diderot. After that, I was a postdoc in the stochastics group at the University of Utah from 2017 until 2020.

I am organizing the Purdue University Probability Seminar this year.

I have research problems available for graduate students at Purdue who are interested in probability.

See Brightspace for course information.

1. Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials with Sean Groathouse and Firas Rassoul-Agha. (2023)
2. Ergodicity and synchronization of the Kardar-Parisi-Zhang equation with Firas Rassoul-Agha and Timo Seppäläinen. (2022)
3. The Green's function of the parabolic Anderson model and the continuum directed polymer with Tom Alberts, Firas Rassoul-Agha, and Timo Seppäläinen. (2022)
4. Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation with Sean Groathouse and Firas Rassoul-Agha. (2021)
5. Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique with Elnur Emrah and Timo Seppäläinen. Probability and Mathematical Physics. 4 (3) 609-666 (2023).
   
6. Tail bounds for the averaged empirical distribution on a geodesic in first-passage percolation with Wai-Kit Lam and Xiao Shen. (2020)
   
7. A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential with Sergazy Nurbavliyev and Firas Rassoul-Agha. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 58(2) pp. 1010-1040.
   
8. Right-tail moderate deviations in the exponential last-passage percolation with Elnur Emrah and Timo Seppäläinen. (2020)
   
9. Geometry of geodesics through Busemann measures in directed last-passage percolation with Firas Rassoul-Agha and Timo Seppäläinen. Journal of the European Mathematical Society. 25 (7) 2573–2639 (2023).
   
10. Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model with Elnur Emrah and Timo Seppäläinen. Electronic Journal of Probability. 26: 1-45 (2021).
    
11. Uniqueness and ergodicity of stationary directed polymer models on the square lattice with Firas Rassoul-Agha. Journal of Statistical Physics. Vol. 179, 672–689 (2020)
    
12. Busemann functions and Gibbs measures in directed polymer models on ℤ² with Firas Rassoul-Agha. Annals of Probability. Vol. 48, No. 2, 778-816. (2020)
    
13. Upper tail large deviations in Brownian directed percolation. Electronic Communications in Probability, 24 no. 45, 1-10. (2019)
    
14. Particle representations for stochastic partial differential equations with boundary conditions. with Dan Crisan and Thomas G. Kurtz Electronic Journal of Probability 23 (65), 1-29. (2018)
    
15. Large deviations for some corner growth models with inhomogeneity. with Elnur Emrah Markov Processes and Related Fields 23, 267-312. (2017)
    
16. Large deviations of the free energy in the O'Connell-Yor polymer. Journal of Statistical Physics 160 (4), 1054-1080. (2015)