We prove distributional convergence a family of random processes on $\mathbb{Z}$, which describe a type of random walk with dependent delay. The model generalizes the "totally asymmetric q-lazy hipster random walk" studied by Addario-Berry et al [PTRF, '20]. We introduce a novel approach which relies on convergence results for finite difference schemes of Hamilton-Jacobi equations. This talk is based on joint work with Louigi Addario-Berry and Erin Beckman.
Department of Mathematics