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Aug 26, 2012 at 18:32 comment added Stéphane Laurent @SIB: I have just added an edit to my post. I think RW is right.
Aug 26, 2012 at 15:05 comment added Stéphane Laurent Correction: sorry, obviously I meant $T$ preserves this measure, not T is invariant...
Aug 26, 2012 at 14:31 comment added Stéphane Laurent Thanks for the reference. Sorry but doing mathematics is not currently my daily job hence I don't have time enough to read many papers. Do you mean $T$ is not invariant with the mesure I proposed ?
Aug 26, 2012 at 13:20 comment added SIB Correction: arxiv.org/pdf/1204.1621.pdf
Aug 26, 2012 at 13:18 comment added SIB @ Stéphane! You cannot start with an arbitrary probability vector (say (1/2, 1/2) and expect to have an invariant measure (see arxiv.org/pdf/0812.1088.pdf for instance). Maybe the following paper would be also interesting for you arxiv.org/pdf/0812.1088.pdf
Aug 26, 2012 at 12:37 comment added Stéphane Laurent Thanks. The invariant measures is the first question of my post. But I think there is a natural fully supported invariant measure and this is the invariant measure in which I am interested: start from the vertex at the top of the graph and go to one of the two possible vertices at next level with probabilities $1/2$ and $1/2$.
Aug 26, 2012 at 12:17 history answered SIB CC BY-SA 3.0