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We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (ALEA Lat. Am. J. Probab. Math. Stat. 20(1):33–51, 2023) to Z2 (for d≥3, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Engländer and Volkov (Coin Turning, Random Walks and Inhomogeneous Markov Chains, World Scientific and Volkov, Singapore, 2025)). This wal
