I am a Master Student at McGill University, working on heights of Random Trees under the supervision of Louigi Addario-Berry.
MSc in Mathematics, Sep 2019 - Apr 2021 (est)
BSc, Joint Honours in Mathematics and Computer Science, Sep 2015 - Apr 2019
We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (Pemantle’s Min-Plus Binary Tree, 2017. arXiv:1709.07849 [math.PR]), and to the critical random hierarchical lattice studied by Hambly and Jordan (Adv Appl Probab 36(3):824–838, 2004. https://doi.org/10.1239/aap/1093962236 ). We prove distributional convergence for the processes, after rescaling, by showing that their evolutions can be understood as a discrete analogues of certain convection–diffusion equations, then using a combination of coupling arguments and results from the numerical analysis literature on convergence of numerical approximations of PDEs.
You can find my formal CV here.