TY - JOUR
T1 - The GHP Scaling Limit of Uniform Spanning Trees in High Dimensions
AU - Archer, Eleanor
AU - Nachmias, Asaf
AU - Shalev, Matan
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/3
Y1 - 2024/3
N2 - We show that the Brownian continuum random tree is the Gromov–Hausdorff–Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus Znd with d>4, the hypercube {0,1}n, and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height and simple random walk on these uniform spanning trees to their continuum analogues on the continuum random tree.
AB - We show that the Brownian continuum random tree is the Gromov–Hausdorff–Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus Znd with d>4, the hypercube {0,1}n, and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height and simple random walk on these uniform spanning trees to their continuum analogues on the continuum random tree.
UR - http://www.scopus.com/inward/record.url?scp=85186573156&partnerID=8YFLogxK
U2 - 10.1007/s00220-023-04923-2
DO - 10.1007/s00220-023-04923-2
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C2 - 38449684
AN - SCOPUS:85186573156
SN - 0010-3616
VL - 405
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
M1 - 73
ER -