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	"review": true,
23	"approval": "first-time"
24	}