Research

(with A. Auffinger and M. Damron) 50 years of first passage percolation. Published in the University Lecture Series of the AMS. An earlier version is available on the arXiv.

• (with S. Chatterjee, P. Chinmay, and P. Sosoe) Robust construction of the incipient infinite cluster in high dimensional critical percolation. arXiv

• (with M. Damron, C. Janjigian, W.-K. Lam, and X. Shen) Estimates for the empirical distribution along a geodesic in first-passage percolation. arXiv

• (with M. Damron, D. Harper, and W.-K. Lam) Exceptional behavior in critical first-passage percolation and random sums. arXiv

• (with D. Ahlberg and C. Hoffman) The number of geodesics in planar first-passage percolation grows sublinearly. arXiv

• (with S. Chatterjee and P. Sosoe) Subcritical Connectivity and Some Exact Tail Exponents in High Dimensional Percolation. Communications in Mathematical Physics. arXiv, journal

• (with M. Damron, D. Harper and W.-K. Lam) Transitions for exceptional times in dynamical first-passage percolation. Probability Theory and Related Fields. arXiv, journal

• (with G. Brito and M. Damron) Absence of backward infinite paths for first-passage percolation in arbitrary dimension. Annals of Probability. arXiv, journal

• (with B. Bock and M. Damron) Random nearest neighbor graphs: the translation invariant case. Annales de l’Institut Henri Poincaré. arXiv, journal

• (with M. Damron and W.-K. Lam) Universality of the time constant for 2D critical first-passage percolation. Annals of Applied Probability.  arXiv, journal

• (with L.-P. Arguin) On absence of disorder chaos for Ising spin glasses on Z^d. Electronic Communications in Probability. arXiv, journal

• (with S. Chatterjee) Restricted percolation critical exponents in high dimensions. Communications on Pure and Applied Mathematics. arXiv, journal

• (with M. Damron, C. Houdré, and C. Xu) Lower bounds for fluctuations in first-passage percolation for general distributions. Annales de l’Institut Henri Poincaré. arXiv, journal

• (with M. Damron and W.-K. Lam) The size of the boundary in first-passage percolation. Annals of Applied Probability. arXiv, journal

• Infinite geodesics, asymptotic directions, and Busemann functions. In Random Growth Models (Proceedings of Symposia in Applied Mathematics 75). arXiv

• (with M. Damron and P. Sosoe) Strict inequality for the chemical distance exponent in two-dimensional critical percolation. Communications on Pure and Applied Mathematics. arXiv, journal

• (with M. Damron and P. Sosoe) Arm events in two-dimensional invasion percolation. Journal of Statistical Physics. arXiv, journal

• (with B. Vollmayr-Lee, R. S. McIsaac, and J. D. Hellerick) Anomalous dimension in a two-species reaction-diffusion system. Journal of Physics A. arXiv, Journal

• (with S. Bhupatiraju and A. A. Járai) Inequalities for critical exponents in d-dimensional sandpiles. Electronic Journal of Probability. arXiv, journal

• (with M. Damron) Bigeodesics in first-passage percolation. Communications in Mathematical Physics. arXiv, journal.

• (with M. Damron and P. Sosoe) On the chemical distance in critical percolation. Electronic Journal of Probability. arXiv, journal

• (with A. Auffinger and M. Damron) Rate of convergence of the mean for sub-additive ergodic sequences. Advances in Mathematics. arXiv, journal

• (with M. Damron and P. Sosoe) Subdiffusive concentration in first-passage percolation. Electronic Journal of Probability . arXiv, journal

• (with M. Damron and P. Sosoe) Sublinear variance in first-passage percolation for general distributions. Probability Theory and Related Fields. arXiv , journal

• (with A. Auffinger and M. Damron) Limiting geodesics for first-passage percolation on subsets of Z^2. Annals of Applied Probability. arXiv, journal

• (with M. Damron and P. Sosoe) Subdiffusivity of random walk on the 2D invasion percolation cluster. Stochastic Processes and their Applications. arXiv, journal

• (with M. Damron) Busemann functions and infinite geodesics in two-dimensional first-passage percolation. Communications in Mathematical Physics. arXiv, journal

• (with M. Damron and P. Sosoe) On the chemical distance in critical percolation II. arXiv