Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 58, Number 3 (2006), 329-357.
On the range of pinned random walks
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.
Tohoku Math. J. (2), Volume 58, Number 3 (2006), 329-357.
First available in Project Euclid: 17 November 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations
Hamana, Yuji. On the range of pinned random walks. Tohoku Math. J. (2) 58 (2006), no. 3, 329--357. doi:10.2748/tmj/1163775134. https://projecteuclid.org/euclid.tmj/1163775134