Uniform Spanning Trees
A spanning tree chosen randomly from among all the spanning trees with equal probability is called a uniform spanning tree (UST). This model has been extensively researched in probability and mathematical physics.
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Famous quotes containing the words uniform and/or trees:
“The sugar maple is remarkable for its clean ankle. The groves of these trees looked like vast forest sheds, their branches stopping short at a uniform height, four or five feet from the ground, like eaves, as if they had been trimmed by art, so that you could look under and through the whole grove with its leafy canopy, as under a tent whose curtain is raised.”
—Henry David Thoreau (1817–1862)
“One wonders that the tithing-men and fathers of the town are not out to see what the trees mean by their high colors and exuberance of spirits, fearing that some mischief is brewing. I do not see what the Puritans did at this season, when the maples blaze out in scarlet. They certainly could not have worshiped in groves then. Perhaps that is what they built meeting-houses and fenced them round with horse-sheds for.”
—Henry David Thoreau (1817–1862)