# Do multiple instances of Mathematica run completely independently?

Let me simplify the problem I am trying to solve so that the issue I face is highlighted.
Say, I want to generate $n$ samples of a Gaussian random variable. I have a script (say random.m) that does it. I have Mathematica installed on a node with $4$ cores. I ssh into it and run $4$ instances of "math -script random.m" The idea is that I generate $\frac{n}{4}$ per instance. Now, my actual script is a little more complicated, with other variable names, etc. One of the features of Mathematica is that the value of a variable is not restricted to a notebook (unless one does so explicitly).
My question basically is: when I run 4 instances of a program, do they run completely independently of one another?
(Even though I have the same variable names in random.m, the variables themselves are random. So, I don't want any cross-talk amongst the four instances.)

-
There are different meanings of independence here. *If you want statistical independence on each node, you can invoke your own different SeedRandom[blah] on each node; they would be independent anyway - but you can control it yourself on each node. *If you seek to run your code faster by running it on 4 independent copies of mma ... then you may be disappointed in this instance ... because, as far as I can tell, mma's Random number generator will automatically take advantage of as many cores as you have available ... so if you run 4 copies of Mma, you still only have 4 cores available. –  wolfies Mar 30 at 17:28