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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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2014, 2014
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| Edition: | 1st ed. 2014 |
| Series: | École d'Été de Probabilités de Saint-Flour
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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