Consider some function $f(E_{1},E_{2})$, say $$ \tag 1 f(E_{1},E_{2}) = \exp[-E_{1}^{3}+E_{2}^{2}] $$ I want to generate random $n$ points $E_{1}$, $E_{2}$ using this function as weights, with an extra condition for the domain of definition of $E_{1},E_{2}$: $$ \tag 2 E_{1}\ge m_{1},\quad E_{2}\ge m_{2}, \quad E_{3} \equiv m-E_{1}-E_{2} \ge m_{3} $$ $$ \tag 3 -1 <\frac{\sqrt{E_{3}^{2}-m_{3}^{2}}-\sqrt{E_{1}^{2}-m_{1}^{2}}-\sqrt{E_{2}^{2}-m_{2}^{2}}}{2\sqrt{E_{1}^{2}-m_{1}^{2}}\sqrt{E_{2}^{2}-m_{2}^{2}}} < 1, $$ where $m,m_{1-3}$ are real positive constants which are known, $m>m_{1}+m_{2}+m_{3}$.
I expect that this may be done using RandomVariate command. However, I face two complications: first, I don't know syntax allowing to use f as the distribution function in RandomVariate, second, I don't know how to implement the domain of definition $(2),(3)$ in RandomVariate.
The example of parameters is m = 10, m1 =2, m2 = 0.5, m3 = 0.1.
Could you please help me with this?
P.S. The second problem may be avoided if just setting f to be zero outside of the range $(1),(2)$. Then, probably, my question may be rephrased on how to create symbolic distribution using Eqs. $(1)-(3)$.
