If your in a hurry and need this today then use something called rejection sampling. Idea is to have any number of random samples and then reject the ones that do not fall into your criteria. Here’s how you could approach this.
Make a random field
make logo transparent and run transparency flattener
subtract and eliminate all paths with more then 4 points.
Now the effect does work better if you have a pattern on the edge of the logo. Like in your example so store the logo path and subtract slightly offset version. and add a scatter stroked edge that has same symbol for more definition.
Final Image: The result after some manual tweaking for a few seconds and a ring of edge points done with a scatter brush.
This is also pretty easy to script.