bibkey: polya1921randomwalk authors: Georg Pólya year: 1921 title: Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz doi: 10.1007/BF01458701 url: https://doi.org/10.1007/BF01458701 claim: Classical recurrence in dimensions one and two and transience from dimension three concerns the simple symmetric nearest-neighbour lattice random walk. strata_touched: [] license: citation-only triage: anchor

Lattice return probability and a specified transport law

The Crossref DOI record identifies Pólya, the German title above and its publication year. The original article interior has not been retrieved, and no original theorem or page numbering is supplied.

The FIB boundary volume §12 includes the Fourier Green-function calculation needed for the simple symmetric nearest-neighbour walk on Z^d. The one-step characteristic function, quadratic singularity and renewal interpretation determine the stated recurrence threshold independently of an original-text locator. This classical attribution supplies no return law for an arbitrary FIB graph or a walk with a different transition kernel.