Oscillation of Metropolis-Hastings and simulated annealing algorithms around LASSO estimator

In this work we study, as the temperature goes to zero, the oscillation of a family of Gibbs measures around LASSO estimator. We derive new criteria for estimating LASSO, choosing the proposal distribution and the temperature in Metropolis-Hastings algorithm. Finally we apply these results to analyse the convergence of Metropolis-Hastings and simulated annealing algorithms.