I am working in the field of mechanical engineering. I am interested in stochastic modelling of structures with n random variables. When looking for specific behaviour of the analyzed mechanical system, I found that vectors of the n random variables associated to this behaviour are clustered in a given area of Rn as shown below for n=3.
I am looking for a way to identify or characterize this potential subspace. Quick numerical analyzes underlined that this subspace is not a vectorial space. Indeed, if a and b are in this space, it is found that a+b is not necessarily in it.
I am looking for ideas in order to mathematically characterize this cluster as I do not believe this can be random.
It's a little unclear from your diagram, but I'd look at this wikipedia page:
https://en.wikipedia.org/wiki/Cone#Equation_form
As Connor said in the comments, it does look like an eliptic cone.
On the other hand, there are a variety of techniques for characterising data by mathematical means. You could look up topological data analysis for information on that.