The harmonic measure of balls in random trees
نویسندگان
چکیده
منابع مشابه
The harmonic measure of balls in random trees
We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius n centered at the root, we prove that, although the size of the boundary is of order n, most of the harmonic measure is supported on a boundary set of size approximately equal to n , where β ≈ 0.78 is a universal constant. To derive such results, we interpret harmonic measure as the exit d...
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We consider simple random walk on the family tree T of a nondegenerate supercritical Galton-Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of T . Concretely, this implies that an exponentially small fraction of the nth level of T carries most of the harmonic measure. First order asymptotics for ...
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We consider simple random walk on a critical Galton–Watson tree conditioned to have height greater than n. It is well known that the cardinality of the set of vertices of the tree at generation n is then of order n. We prove the existence of a constant β ≈ 0.78 such that the hitting distribution of the generation n in the tree by simple random walk is concentrated with high probability on a set...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2017
ISSN: 0091-1798
DOI: 10.1214/15-aop1050