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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 58 NO.3 / (2006))
On the range of pinned random walks
Yuji Hamana,
Pages. 329-357
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.
Contents 1. Preliminaries and notation
2. Main results
3. Proof of Proposition 2.1 and Theorem 2.2
4. Proof of Theorem 2.3
5. Large deviations in the upward direction
Key words Pinned random walks, law of large numbers, large deviations
Mathmatical Subject Classification 60G50, 60F05, 60F10