Appears in collections : 2017 - T2 - Stochastic dynamics out of equilibrium, SRS Varadhan: The role of topology and compactness in the theory of large deviations

The role of topology and compactness in the theory of large deviationsWhen a large deviation result is proved there is some topology involved in the statement because it affects the class of sets for which the estimates hold. Often the choice is natural and obvious. There may be a stronger topology in which the theory holds. This requires additional work and we may or may not be inclined to do it. However the application we have in mind might require it, in which case we have no choice. It is also possible that the the principle fails in the familiar strong topology and the weak topology is not sufficient to prove the result. Then we have to invent a new topology. We will look at some examples to illustrate these points.