Tohoku Mathematical Journal
2006
September
SECOND SERIES VOL. 58, NO. 3

Tohoku Math. J.
58 (2006), 329-357

Title ON THE RANGE OF PINNED RANDOM WALKS

Dedicated to Professor Tokuzo Shiga on his sixtieth birthday
Author Yuji Hamana

(Received September 2, 2004, revised April 20, 2005)
Abstract. The range of random walks means the number of distinct sites visited at least once by the random walk. In two-or-more-dimensional cases, we established the law of large numbers for the range of simple symmetric random walks under the conditional probability given the event that the last point is the origin. Moreover we studied the large deviations in the upward direction and obtained similar results to the original random walk.

2000 Mathematics Subject Classification. Primary 60G50; Secondary 60F05, 60F10.
Key words and phrases. Pinned random walks, law of large numbers, large deviations.

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