Random Walks in Varying Dimensions

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two symmetric step distributions of bounded support. Mathematical Sciences Institute, 409 College Ave., Ithaca, NY, 14853. 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 # DMS 9300191, by a Sloan Foundation Fellowship, and by a Presidential Faculty Fellowship. Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706 . Department of Statistics, 367 Evans Hall University of California, Berkeley, CA 94720. Research partially supported by NSF grant # DMS-9404391 and by a Junior Faculty Fellowship from the Regents of the University of California.