The HAXM memory limit has to cover more than the memory assigned to you virtual device.
According to the log above, the amount of memory assigned to the device ("AVD RAM size", set to 1536MB) exceeds the memory limit of HAXM ("Max RAM size", currently set to 512MB). You have to adjust that: by running the HAXM installer, you can set the "Max RAM size" limit to 2048MB (or more should your physical machine be able to handle that) instead of the 512MB currently handled.
-> HAXM installer documentation: for Windows - for MacOS X
If your physical machine cannot afford assigning 2048MB or more to HAXM, assign as much as you reasonably can to HAXM (mine is 1024MB), and assign less memory to your virtual device. Be careful though, on my side I couldn't have a API 23 emulator running well with less than 768MB assigned (and 64MB for the heap).
-> To change the memory settings of your virtual device, you have to go to the "Android Virtual Device (AVD) Manager", and then to edit your device. I highlighted this in the picture below.

I'm using Eclipse, but the process should be similar under Android Studio.