Explore high-precision estimation techniques for random walks in constrained memory environments through this 25-minute IEEE conference talk. Delve into the comparison of RL and L using pseudorandom generators and graph algorithms, with a focus on directed graphs and Laplacians. Learn about solving Laplacian systems and their application in deterministic algorithms for ERWP. Examine the Eulerian case of ERWP via Laplacians and understand the algorithm outline. Investigate unit circle approximation and its definition for Laplacian matrices. Discover derandomization methods using Laplacian solvers and consider open problems and future research directions in this field.