Anomalous recurrence properties of many-dimensional zero-drift random walks

  title={Anomalous recurrence properties of many-dimensional zero-drift random walks},
  author={Nicholas Georgiou and Mikhail Menshikov and Aleksandar Mijatovi{\'c} and Andrew R. Wade},
  journal={Advances in Applied Probability},
  pages={99 - 118}
Abstract 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. We study a family of zero-drift spatially nonhomogeneous random walks (Markov processes) whose increment covariance matrix is asymptotically constant along rays from the origin, and which, in any ambient dimension d≥2, can be adjusted so… 
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