Online minimum spanning trees with random edge weights

Prove that the optimal expected cost of building a spanning tree online, with random edge weights, converges, and find the limit.

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "probability",
	5	+ "graph-theory"
	6	+ ],
	7	+ "type": "proof",
	8	+ "also": [
	9	+ "construction"
	10	+ ],
	11	+ "source": {
	12	+ "key": "aldous",
	13	+ "name": "David Aldous's open problems",
	14	+ "url": "https://www.stat.berkeley.edu/~aldous/Research/OP/online_zeta3.html",
	15	+ "id": "online_zeta3",
	16	+ "curator": "David Aldous",
	17	+ "poser": "David Aldous, Omer Angel and Nathanael Berestycki",
	18	+ "status": "open",
	19	+ "as_of": "2026-10-20",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}