Two-Dimensional Random Walk : Cambridge University Press : 9781108472456 : 1108472451 : 18 Mar 2021 : "The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. The book starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. Then, after reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements -- which can be viewed as a "canonical soup" of nearest-neighbour loops through infinity -- again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks -- which are the "noodles" in the soup -- and also discover how Poisson processes of infini