A Discrete Analogue of a Theorem of Makarov
1993 ◽
Vol 2
(2)
◽
pp. 181-199
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Keyword(s):
A theorem of Makarov states that the harmonic measure of a connected subset of ℝ2 is supported on a set of Hausdorff dimension one. This paper gives an analogue of this theorem for discrete harmonic measure, i.e., the hitting measure of simple random walk. It is proved that for any 1/2 < α < 1, β < α − 1/2, there is a constant k such that for any connected subset A ⊂ ℤ2 of radius n,where HA denotes discrete harmonic measure.
1995 ◽
Vol 15
(3)
◽
pp. 593-619
◽
Keyword(s):
1962 ◽
Vol 58
(4)
◽
pp. 708-709
◽
Keyword(s):
1976 ◽
Vol 13
(02)
◽
pp. 355-356
◽
2000 ◽
Vol 16
(3-4)
◽
pp. 399-406
1995 ◽
Vol 15
(1)
◽
pp. 77-97
◽
2010 ◽
Vol 149
(2)
◽
pp. 351-372