×

zbMATH — the first resource for mathematics

Excited random walk. (English) Zbl 1060.60043
Summary: A random walk on \(\mathbb Z^d\) is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on \(\mathbb Z^d\) is transient iff \(d>1\).

MSC:
60G50 Sums of independent random variables; random walks
60K37 Processes in random environments
PDF BibTeX Cite
Full Text: DOI EuDML arXiv