Maximal flow through oriented percolation as p tends to 1

Prove that the deficit of maximal flow through oriented bond percolation behaves like sqrt(2(1 − p)) as p tends to 1.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"probability",
5	"statistical-mechanics"
6	],
7	"type": "proof",
8	"source": {
9	"key": "aldous",
10	"name": "David Aldous's open problems",
11	"url": "https://www.stat.berkeley.edu/~aldous/Research/OP/hammersley_flow.html",
12	"id": "hammersley_flow",
13	"curator": "David Aldous",
14	"poser": "David Aldous and Jason Lenderman",
15	"status": "open",
16	"as_of": "2026-10-20",
17	"catalog": "0521c19bbd38"
18	},
19	"review": true,
20	"approval": "first-time"
21	}