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Introduction
Part I The basic model
Introduction to Part I
The basic model, definitions and results
Regularity properties of the barriers
Lipschitz and L1 estimates
Mass transport inequalities
The limit theorems on barriers
Brownian motion and the heat equation
Existence of optimal sequences
Proof of the main theorem
The basic particle model and its hydrodynamic limit
Part II Variants of the basic model
Introduction to Part II
Independent walkers with current reservoirs
Beyond diffusive scaling
Other models.

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