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

• Κύριος συγγραφέας: Kumagai, Takashi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Lecture Notes in Mathematics, 2101
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.