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My understanding is that the evolution of the wave function is deterministic. Upon measurement, the wave function collapses to an eigenstate of the measurement operator. Which eigenstate is observed is random, with probability based on the corresponding eigenvalue. So the measurement process/wave function collapse is random.

Admittedly it's been a long time since I've studied quantum mechanics! Has the thinking changed?

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Yes, that's basically the Copenhagen interpretation of quantum mechanics, and a perfectly valid way to interpret the math.

The Many Worlds interpretation doesn't have the collapse, it says that all the possibilities happen.

https://en.wikipedia.org/wiki/Many-worlds_interpretation

> In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic.

There's some wrinkles in that interpretation to preserve the Born rule of observed frequencies.

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