Remarks on renewal theory for percolation processes
Keyword(s):
We extend some results of Hammersley and Welsh concerning first-passage percolation on the two-dimensional integer lattice. Our results include: (i) weak renewal theorems for the unrestricted reach processes; (ii) an L1-ergodic theorem for the unrestricted first-passage time from (0, 0) to the line X = n; and (iii) weakening of the boundedness restrictions on the underlying distribution in Hammersley and Welsh's weak renewal theorems for the cylinder reach processes.
1976 ◽
Vol 13
(02)
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pp. 290-300
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1977 ◽
Vol 9
(01)
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pp. 38-54
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1992 ◽
Vol 6
(4)
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pp. 561-580
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1976 ◽
Vol 13
(01)
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pp. 27-38
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1993 ◽
Vol 30
(04)
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pp. 851-862
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1994 ◽
Vol 7
(3)
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pp. 457-464
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2001 ◽
Vol 33
(3)
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pp. 652-673
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