TY - JOUR
T1 - The diameter of uniform spanning trees in high dimensions
AU - Michaeli, Peleg
AU - Nachmias, Asaf
AU - Shalev, Matan
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/2
Y1 - 2021/2
N2 - We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Θ(n). In particular this result applies to expanders, finite tori Zmd of dimension d≥ 5 , the hypercube { 0 , 1 } m, and small perturbations thereof.
AB - We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Θ(n). In particular this result applies to expanders, finite tori Zmd of dimension d≥ 5 , the hypercube { 0 , 1 } m, and small perturbations thereof.
UR - http://www.scopus.com/inward/record.url?scp=85092111417&partnerID=8YFLogxK
U2 - 10.1007/s00440-020-00999-2
DO - 10.1007/s00440-020-00999-2
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AN - SCOPUS:85092111417
SN - 0178-8051
VL - 179
SP - 261
EP - 294
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 1-2
ER -