We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a “meta-stable set.” In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.
"Pointwise estimates and exponential laws in metastable systems via coupling methods." Ann. Probab. 40 (1) 339 - 371, January 2012. https://doi.org/10.1214/10-AOP622