Tohoku Mathematical Journal

On the range of pinned random walks

Yuji Hamana

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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.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 3 (2006), 329-357.

Dates
First available in Project Euclid: 17 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1163775134

Digital Object Identifier
doi:10.2748/tmj/1163775134

Mathematical Reviews number (MathSciNet)
MR2273274

Zentralblatt MATH identifier
1112.60041

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

Keywords
Pinned random walks law of large numbers large deviations

Citation

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


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