On the range of pinned random walks

Yuji Hamana
2006 Tohoku mathematical journal  
×ØÖ Øº The range of random walks means the number of distinct sites visited at least once by the random walk before time n. 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 the similar results to the original random walk. 2000 Mathematics Subject Classification.
more » ... t Classification. Primary 60G50; Secondary 60F05, 60F10. Key words and phrases. pinned random walks, law of large numbers, large deviations. Typeset by A M S-T E X
doi:10.2748/tmj/1163775134 fatcat:i67bgcgyzrbyxnfvzjzbad5oz4