Bénédicte Haas, University of Paris-Dauphine, France Limits of Non-increasing Markov Chains and Applications to Random Trees and Coalescents Consider a non-increasing Markov chain with values in the set of non-negative integers, starting from a large integer !. We describe its scaling limit as ! → ∞, under the assumption that the large jump events are rare and happen at rates that behave like a...

We give an example of a transient reversible Markov chain that a.s. has only a finite number of cutpoints. We explain how this is relevant to a conjecture of Diaconis and Freedman and a question of Kaimanovich. We also answer Kaimanovich’s question when the Markov chain is a nearest-neighbor random walk on a tree.

We introduce inhomogeneous parsimonious Markov models for modeling statistical patterns in discrete sequences. These models are based on parsimonious context trees, which are a generalization of context trees, and thus generalize variable order Markov models. We follow a Bayesian approach, consisting of structure and parameter learning. Structure learning is a challenging problem due to an over...

We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a ...

In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. This provides a basic unification of both data parallel divisible load scheduling and Markov chain models for the first time in 16 years of research. Such equivalence is demonstrated for divisible scheduling on linear daisy chains and single and two level tree netw...

This paper considers the problem of veriication of proba-bilistic systems, for both the discrete-and real-time cases. Probabilistic systems are modeled as Markov chains, concurrent Markov chains (i.e. MCs with non-determinism) or, in the real-time case, generalized semi-Markov processes (Markovian processes with time delays on events). Discrete-time speciications are described in the logics PTL...

We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a ...

We consider the problem of inferring an ancestral state from observations at leaves a tree, assuming evolves along tree according to two-state symmetric Markov process. establish general branching rate condition under which maximum parsimony, common reconstruction method requiring only knowledge topology (but not substitution rates or other parameters), succeeds better than random guessing unif...