I am a graduate student and I am writing a paper.
For an irreducible Markov chain $P$ with spectral radius $\rho$, the historial literature says that it is $\rho$-transient iff its Green function at $1/\rho$ is finite.
My problem: in my paper, I am going to discuss several different Markov chains with distinguished spectral radii, it is inconvenient for me to decribe every Markov chains $P$ to be $\rho(P)$-transient (If I define the $\rho(P)$ to be its sepctral radius).
The most convenient way for me is that I expect a new name which is just the property to describe the Markov chains whose Green function at the reciprocal of its spectral radius is finite without mentioning the value of spectral radius or the Markov chain itself.
I want to give a new name to $\rho$-transience like 'spectral-transience', 'spectral-radius-transience' or 'rho-transience'.
How do you think these names or is there better names suggested? And generally saying is that acceptable to give a new name for personal convenience?
(I will mention the historical literatures which introduced and discussed this concept and the name over there when I am giving the definition.)