A. Bovier, M. Eckho, V. Gayrard, and M. Klein \Metastability and low-lying spectra in reversible Markov chains", Commun. Math. Phys. 228, 219-255 (2002).  Home/Search   Document Not in Database   Summary   Related Articles

....in principle allow to justify such expansions, their implementation seems rather tedious and has not been carried out to our knowledge. Here we will resort to a di erent approach that combines ideas already suggested in [W1] with potential theoretic ideas. In fact, this approach was developed in [BEGK2] in the setting of discrete Markov chains, where indeed many technical problems we will be facing here disappear, and that may serve as a nice introduction. We will from now on assume that F is at least three times continuously di erentiable and has a nite set of local minima, which we denote by ....

....(1.5) state that all valleys of F have di erent depth , which is in some sense the generic situation. In this case a number of simpli cations take place, in particular we do not have to deal with degenerate eigenvalues. These conditions are completely analogous to the conditions imposed in [BEGK2]. Our general approach does, however, in principle also allow to treat degenerate situations. We postpone the treatment of such cases to future work. In the course of the proof of Theorem 1.1 we will also obtain rather detailed control on the eigenfunctions of L corresponding to its small ....

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A. Bovier, M. Eckho, V. Gayrard, and M. Klein \Metastability and low-lying spectra in reversible Markov chains", Commun. Math. Phys. 228, 219-255 (2002).

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