Illustrator-recreate similar effects gradient

Hi everyone,

There are quite a few questions across the forums about gradients but I have not seen any that is close to what I want to create.

I have attached a pic for reference. Basically I am wondering how to create the white vertical soft strips. I have tried creating a white line and gaussian blur but not as close. Does anyone have an alternative method?

Another qns, the circles can be created using a scatter brush, how do you make the opacity appear random without having to click each obj and adjust its opacity?