Anomalous recurrence properties of many-dimensional zero-drift random walks
(2016)
Journal Article
Georgiou, N., Menshikov, M. V., Mijatovic, A., & Wade, A. R. (2016). Anomalous recurrence properties of many-dimensional zero-drift random walks. Advances in Applied Probability, 48(Issue A), 99-118. https://doi.org/10.1017/apr.2016.44
Famously, a d-dimensional, spatially homogeneous random walk whose increments are nondegenerate, have finite second moments, and have zero mean is recurrent if d∈{1,2}, but transient if d≥3. Once spatial homogeneity is relaxed, this is no longer true... Read More about Anomalous recurrence properties of many-dimensional zero-drift random walks.