On sequences of records generated by planar random walks

We investigate the statistics of three kinds records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers these grow as universal power laws time, respective exponents 1/4, 1/3 1/2. study diagonal relies on underlying renewal structure successive hitting times locations translated copies a fixed target. In this sense, work represents two-dimensional extension analysis made by Feller ladder points, i.e., for one-dimensional walks. This approach yields variety analytical asymptotic results, including full records, joint law epoch location current record angular distribution record. sequence cannot be constructed in terms process. spite this, their number is shown to super-universal square-root isotropic walks any spatial dimension. Their also obtained. Higher-dimensional are briefly discussed.