There is a similar question on SE.
I would be surprised if there was any Buddhist reference supporting Schopenhauer's claim that "the world came into being as a result of some disturbance in the heavenly calm of Nirvana." To me, this statement even sounds "plain weird."
Samsara refers to two phenomena:
- A place
- The contaminated aggregates
In Buddhism, the expression "the world" might refer to either, depending on the context. See another question/answer on SE on this matter. In either case, although it is said that the world is produced due to karma and afflictions, it is usually said to be without beginning. There are countless traditional texts and authoritative teachings establishing this statement. Here are a few:
In Cutting the Root of Samsara, Lama Zopa Rinpoche says:
[Suffering] comes from the past karma created by the self-cherishing thought and it is also dependent on our present-life attitude as well. From beginningless rebirth, it's been like this.
The Abhidharma Sutra says:
It is said: "Though beginningless, it entails an end - What is naturally pure and consists of permanent dharmas Is not seen, since it is obscured by a beginningless cocoon[...]
The third Karmapa's commentary to it reads:
Consequently, though samsara is beginningless, once the reality[...]
There are four types of nirvana. Without going in details, nirvana is the final analytical cessation achieved in dependence upon a union of calm abiding (shamata) and special insight (actual vipassana) directly apprehending the nature of reality, emptiness. According to Mahayana, abiding nirvana is the complete and definitive abandonment of afflictive obscurations while non-abiding nirvana is the complete and definitive abandonment of afflictive and knowledge obscurations. There is no disturbance "in" nirvana.
It is definitely not like we ever abided in nirvana and subsequently "fell" from it. There is no such "genesis" in Buddhism.