TITLE: Lower bound on the entries of the Perron vector
QUESTION [7 upvotes]: Let $A$ be a matrix that satisfies all the conditions of Perron- Frobenius theorem. From the theorem it is known that the entries of the eigenvector corresponding to the largest eigenvalue will be strictly positive. Are their any good lowerbounds known for these entries ? (Assuming that the eigenvector is normalized in some suitable way) 
Imagining $A$ as some kind of a Markov chain, I would expect the lowerbound to depend on how the vertex corresponding to the   entry in question is connected to other verticies (degree, weight of self-loops etc.). Any results along those lines would be very-helpful

REPLY [5 votes]: This seems to be answered in the accepted answer to this question: The height of the Perron-Frobenius eigenvector
For convenience, here is the estimate: