Stochastic Spatial Models: A Hyper-Tutorial

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A. Basic Definitions

  1. Notation, lattices, and neighbors
  2. Continuous time Markov chains
  3. Distributions, Stationarity
  4. Coexistence and Related Concepts

B. Genetics: Voter Models

  1. Coexistence or Consensus?
  2. One Dimension
  3. Coalescing Random Walks
  4. Hybrid zones: Inferior Heterozygotes

C. Growth Models

  1. Richardson's model
  2. Biased voter model
  3. Contact process
  4. Long Range Limits
  5. Quadratic birth rates
  6. Rapid Stirring Limits
  7. Nonlinear voter model

Multitype Models (The Big Picture)

D. Case 1. Attracting Fixed Point

  1. Grass-bushes-trees
  2. Competition of species
  3. Predator-prey system
  4. Predator-mediated coexistence

E. Case 2. Bistability

  1. Competing contact processes
  2. Colicin
  3. Catalyst Surface

F. Case 3. Cyclic Systems

  1. Epidemic models
  2. Multitype biased voter model l
  3. Nonlinear predator-prey system

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