e.g. What the percussionist plays on the Seaside version of Hope Day at 4:15
The rhythm in the part of the song you link doesn't seem random at all. It's moderately complex, but for sure can be perfectly notated and read.
However, to try to answer the question, you can write ad libitum which means "as desired" to indicate you give the performer freedom in how to perform some section of music. This term however can be interpreted in many ways, so you may want to add some explanation or suggestion of what you mean exactly. For example tempo ad libitum would mean one can play at any tempo they like, while solo ad libitum means to improvise a solo. At this stage you can get as creative as you like, you can add your own graphic marks to inspire the performer, but be aware they may play something very different from what you thought about!
See also: https://en.wikipedia.org/wiki/Ad_libitum