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

• Main Author: Kumagai, Takashi (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Lecture Notes in Mathematics, 2101
• Subjects: Mathematics.; Potential theory (Mathematics).; Probabilities.; Discrete mathematics.; Mathematical physics.; Probability Theory and Stochastic Processes.; Mathematical Physics.; Potential Theory.; Discrete Mathematics.

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...

Table of Contents:

• 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.