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	+}