Hedge Fund Trading infrastructure

I am kind of a novice in finance and I am slightly confused about the different between firms such as DE Shaw and Rentech that practices statistical arbitrage and various trading strategies vs prop-trading firms like Jane Street etc.

Do hedgefunds that use quantitative approaches and automated trading such as DE Shaw and Rentech have their own infrastructure for trading with the exchanges like prop-trading firms or do they, like retail investors, borrow the trading infrastructure of other firms with membership on exchanges or part of an ATS?

If they don't have direct access to exchanges like some quantitative prop firms, how would they execute things like high-frequency trading or take advantage of arbitrage opportunities that exist for very short times?

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