Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 54--66

ON A SELF-AVOIDING RANDOM WALK

By

THOMAS KUCZEK, Purdue University

and

KEITH CRANK, National Science Foundation

SUMMARY. A self-avoiding random walk on Z1 is considered. By conditioning on certain points with regeneration type properties called "break points", it is shown that the set of occupied points grows in a linear fashion. The utility of break points is that they greatly simplify the conditioning involved in studying the process.

AMS (1980) subject classification. Primary 62K35.

Key words and phrases. Random walk, break points.

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