Random Walks on Disordered Media and their Scaling Limits École d'Été de Probabilités de Saint-Flour XL - 2010 /

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. T...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kumagai, Takashi (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:École d'Été de Probabilités de Saint-Flour ; 2101
Temas:
Probabilities.
Mathematical physics.
Potential theory (Mathematics).
Discrete mathematics.
Probability Theory.
Mathematical Physics.
Potential Theory.
Discrete Mathematics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Introduction
  • Weighted graphs and the associated Markov chains
  • Heat kernel estimates - General theory
  • Heat kernel estimates using effective resistance
  • Heat kernel estimates for random weighted graphs
  • Alexander-Orbach conjecture holds when two-point functions behave nicely
  • Further results for random walk on IIC
  • Random conductance model.

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