Graduate Probability Seminar

Title: Capacity for Random Walks

Abstract: For random walks on d>=3 (transient case), we can measure how “approachable” a finite set A is from infinity by defining its capacity. For this talk I will introduce the definition of capacity, its properties, estimations, and related examples. Those results provide a probabilistic view of many problems from the electrical network theory. If time allows, I will also introduce the concept of capacity for recurrent random walks.

References: Lawler, G. F., & Limic, V. (2010). Random Walk: A Modern Introduction, Chapter 6. Cambridge: Cambridge University Press.