On new operating systems process address space is pieced together independently from physical space. So you can have contiguous, multi-GB array even if you don't have contiguous, multi-GB physical region.

As you read/write your virtual address space the CPU detects that there is no TLB mapping and interrupts into operating system which behind the scenes finds a page, returns the mapping and continues as if nothing ever happened.

This is why a process nowadays can allocate any amount of memory -- more than there is physical memory on the machine. It only starts grinding to a halt when you actually try to use it all. (This actually is one of my interview questions -- Can a process allocate more memory than is physically available on the machine? Why does it work?)