Jordan blocks in a one-dimensional Markov map

Adjoint Jordan Blocks

Let G be a quasisimple algebraic group over an algebraically closed field of characteristic p > 0. We suppose that p is very good for G; since p is good, there is a bijection between the nilpotent orbits in the Lie algebra and the unipotent classes in G. If the nilpotent X ∈ Lie(G) and the unipotent u ∈ G correspond under this bijection, and if u has order p, we show that the partitions of ad(X...

Jordan blocks and strong irreducibility

An operator is said to be strongly irreducible if its commutant has no nontrivial idempotent. This paper first shows that if an operator is not strongly irreducible then the set of idempotents in its commutant is either finite or uncountable. The second part of the paper focuses on the Jordan block which is a well-known class of irreducible operators, and determines when a Jordan block is stron...

One-dimensional bargaining with Markov recognition probabilities

We study a process of bargaining over alternatives represented by points in the unit interval. The identity of the proposer is determined by a general Markov process and the acceptance of a proposal requires the approval of it by all the players. We show that for every value of the continuation probability below one the subgame perfect equilibrium in stationary strategies is essentially unique ...

One dimensional completely asymmetric Markov processes

In the early 50’s, Feller characterized fully the analytical structure of one dimensional diffusion processes. In particular, he constructed their Green functions in terms of the two positive fundamental solutions of a second order differential equations. He also characterized completely the Laplace transform of their first exit times from an interval in terms of these two fundamental solutions...

Induced Maps , Markov Extensions and Invariantmeasures in One - Dimensional Dynamics