Metastability: A Potential-Theoretic Approach

Part I Introduction.- 1.Background and motivation.- 2.Aims and scopes.- Part II Markov processes 3.Some basic notions from probability theory.- 4.Markov processes in discrete time.- 5.Markov processes in continuous time.- 6.Large deviations.- 7.Potential theory.- Part III Metastability.- 8.Key definitions and basic properties.- 9.Basic techniques.- Part IV Applications: Diffusions with small noise.- 10.Discrete reversible diffusions.- 11.Diffusion processes with gradient drift.- 12.Stochastic partial differential equations.- Part V Applications: Coarse-graining at positive temperatures.- 13.The Curie-Weiss model.- 14.The Curie-Weiss model with a random magnetic field: discrete distributions.- 15.The Curie-Weiss model with random magnetic field: continuous distributions.- Part VI Applications: Lattice systems in small volumes at low temperatures.- 16.Abstract set-up and metastability in the zero-temperature limit.- 17.Glauber dynamics.- 18.Kawasaki dynamics.- Part VII Applications: Lattice systems in large volumes at low temperatures.- 19.Glauber dynamics.- 20.Kawasaki dynamics.- Part VIII Applications: Lattice systems in small volumes at high densities.- 21.The zero-range process.- Part IX Challenges.- 22.Challenges within metastability.- 23.Challenges beyond metastability.- References.-Glossary.- Index.