Contents §1. Introduction 1.1. History 1.2. About the main result §2. Homogeneous walks: one-sided environment 2.1. Definitions 2.2. Classification 2.3. Invariant measures 2.4. One-dimensional case 2.4.1. (+)-measures 2.4.2. (–)-measures 2.4.3. (0)-measures 2.5. ( + , + , ... , +)-measures 2.6. Coexistence of different measure types 2.7. Main uniqueness result 2.8. About explicit formulae 2.8.1. One dimension 2.8.2. Simple invariant measures 2.8.3. General case §3. EIRW in 
3.1. Definitions 3.2. Induced chains 3.3. One-dimensional case 3.3.1. Transient case 3.3.2. Ergodic case 3.3.3. The case of null recurrence 3.3.4. Absence of SIC 3.4. Escape to infinity along the interior 3.5. Invariant measures for the induced chains 3.6. Euler limit 3.7. Escape to infinity along a face §4. Macroprocesses on 
4.1. Scaled dynamics on the measure bundle 4.2. Collision operators in the 2-dimensional case 4.3. Deterministic reflections 4.4. Classification theorem in 2 dimensions 4.5. Local Lyapunov functions 4.6. General definition of collision operators §5. Macroprocesses on compact measure bundles 5.1. Main theorem §6. Applications 6.1. Applications - non-commutative groups 6.2. Other environments 6.2.1. Double-sided evolution 6.3. Random Turing machine 6.4. Multiclass queuing networks 6.5. Neural networks
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