  We consider the first exit point distribution from a bounded domain $\Omega$
of the stochastic process $(X_t)_{t\ge 0}$ solution to the overdamped Langevin
dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t$$ starting from the
quasi-stationary distribution in $\Omega$. In the small temperature regime
($h\to 0$) and under rather general assumptions on $f$ (in particular, $f$ may
have several critical points in $\Omega$), it is proven that the support of the
distribution of the first exit point concentrates on some points realizing the
minimum of $f$ on $\partial \Omega$. The proof relies on tools to study
tunnelling effects in semi-classical analysis. Extensions of the results to
more general initial distributions than the quasi-stationary distribution are
also presented.
