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Length minimizing Hamiltonian paths for symplectically aspherical manifolds

Ely KermanFrançois Lalonde — 2003

Annales de l’institut Fourier

In this note we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Polterovich and Schwarz, we study the role, in the Floer complex of the generating Hamiltonian, of the global extrema which remain fixed as the time varies. Our main result determines a natural condition which implies that the corresponding path minimizes the positive Hofer length. We use this to prove that a quasi-autonomous Hamiltonian...

Stopping Markov processes and first path on graphs

Giacomo AlettiEly Merzbach — 2006

Journal of the European Mathematical Society

Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....

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