Abstract
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogeneous random walks in the plane which interlace two symmetric step distributions of bounded support.
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References
Benjamini, I., Pemantle, R., and Peres, Y. (1994). Martin capacity for Markov chains.Ann. Probab., (to appear).
Durrett, R., Kesten, H., and Lawler, G. (1991). Making money in fair games. In:Random walks, particle systems and percolation, Durrett, and Kesten, (eds.), Birkhäuser: New York.
Kochen, S. and Stone, C. (1964). A note on the Borel-Cantelli Lemma.Illinois J. of Math. 8, 248–251.
Lyons, T. (1983). Transience of reversible Markov chains.Ann. Prob. 11, 393–402.
Scott, D. (1990). A non-integral-dimensional random walk.J. Th. Prob. 3, 1–7.
Spitzer, F. (1964).Principles of Random Walk. Van Nostrand, New York.
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Research partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.
Research supported in part by National Science Foundation Grant No. DMS 9300191, by a Sloan Foundation Fellowship, and by a Presidential Faculty Fellowship.
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Benjamini, I., Pemantle, R. & Peres, Y. Random walks in varying dimensions. J Theor Probab 9, 231–244 (1996). https://doi.org/10.1007/BF02213742
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DOI: https://doi.org/10.1007/BF02213742