Metastability by Anton Bovier & Frank den Hollander

Author:Anton Bovier & Frank den Hollander
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Inserting these bounds into (11.2.37), we arrive at

(11.2.39)

Choosing, as before, , we see that to leading order (11.2.39) coincides with the upper bound (11.2.26), which proves Theorem 11.2 for the case saddle points in the essential gate.

The generalisation to the case of several saddle points in the essential gate is straightforward and is left to the reader. □

11.2.4 Metastable exit times and capacities

In Propositions 11.7–11.8 below we compute the mean value of certain metastable exit times in terms of capacities. At the end we use these propositions to prove Theorem 11.2.

Proposition 11.7

Let be a (non-degenerate quadratic) critical point of , and let be disjoint closed sets. Then there exists an such that

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