I'm hoping someone can explain how I would recreate the outer effect in the attached image in Illustrator. Any help would be appreciated. Thanks!
Create a scatter brush from a raster image. Use a Photoshop brush to create the source raster image. Trace it in Illustrator, choose the "ignore white" option in the Trace options, then Expand the Trace. Then drag it into the Brushes pallet. Choose Scatter Brush as the type of brush, and apply the settings shown below, or adjust to your liking.
Apply the scatter brush to your graphic, and change the stroke to white.