The diameter of uniform spanning trees in high dimensions

Peleg Michaeli; Asaf Nachmias; Matan Shalev

doi:10.1007/s00440-020-00999-2

The diameter of uniform spanning trees in high dimensions

Peleg Michaeli, Asaf Nachmias, Matan Shalev

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	261-294
Number of pages	34
Journal	Probability Theory and Related Fields
Volume	179
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-020-00999-2
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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title = "The diameter of uniform spanning trees in high dimensions",

abstract = "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.",

author = "Peleg Michaeli and Asaf Nachmias and Matan Shalev",

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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.

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The diameter of uniform spanning trees in high dimensions

Abstract

All Science Journal Classification (ASJC) codes

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