AWS Direct Connect - Router at the Co-Lo belongs to whom?

I've been watchin a video from Amazon on AWS Direct Connect. I see that a direct connection is made from Amazon Direct Connect PoP to a router in a co-location facility. The from there there is a circuit (say 1Gbps or 10Gbps) to the enterprise itself. The presentation at turns talked about the carrier owning the (a?) router and the customer owning the router. In the diagram attached below - the device labeled "Customer Gateway" is generally owned and configured by the end customer/user of Amazon Web Services? Or is that more typically owned by the carrier that is providing the data circuit? And finally if the carrier owns that device do they configure it or leave that to the customer? Thank you for clarifying this point for me.
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