According to my test, the stand alone app uses the sames amount of java heap memory than your MATLAB preferences.
To set the amount of Java heap memory you can either uses the menu in the toolstrip
Menu Preferences -> General - Java Heap Memory
or edit the file prefernce file
the put desired amount of the memory in Mb in the line (here 1Gb)
Then compile your app
On Windows platform if you want to change the Heap after compilation. Run the app once then close it. then goes the folder
where XXX is the user name, M.N, APPNAME depends on your MCR version and application name, edit the line
then relauch your app.