UNIFORM SPANNING FORESTS OF PLANAR GRAPHS

被引：4
|
作者：
Hutchcroft, Tom [1 ]
Nachmias, Asaf [2 ]
机构：
[1] Univ Cambridge, DPMMS, Statslab, Cambridge CB3 0WB, England
[2] Tel Aviv Univ, Dept Math Sci, IL-6997801 Tel Aviv, Israel
来源：
FORUM OF MATHEMATICS SIGMA | 2019年 / 7卷
关键词：
60D05 (primary); 05C10 (secondary); ERASED RANDOM-WALKS; GROWTH EXPONENT; CIRCLE PACKING; CONVERGENCE;
D O I：
10.1017/fms.2019.14
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We provide a quantitative form of this result, calculating the critical exponents governing the geometry of the uniform spanning forests of transient proper plane graphs with bounded degrees and codegrees. We find that the same exponents hold universally over this entire class of graphs provided that measurements are made using the hyperbolic geometry of their circle packings rather than their usual combinatorial geometry.
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页数：55
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