Title of the course: Random Walks on Graphs and Networks
Instructor: Mr. Arif Mardin
Dates: 28 August – 10 September 2017
Prerequisites: Familiarity with the basic probability theory on discrete spaces as well as finite Markov chains would be very useful.
Level: Graduate, advanced undergraduate
Abstract: A short abstract or a daily curriculum: The aim of this course is to explain the relationship between the random walks on
discrete spaces, electric networks and lattice models of statistical mechanics. A classic result of Polya on random walks and its connection with
electric networks will be developed. The final part of the course will be devoted to the analysis of various models of statistical mechanics, such as
the Ising and percolation models
Language: TR, EN
Textbook or/and course webpage:
i) P.Doyle, L.Snell: “Random Walks and Electric Networks”, Mathematical Association of America, 1984; the book is available on the Web;
ii) G:Grimmett: ”Probability on Graphs”, Cambridge University Press, 2010;
iii) R.Lyons, Y.Peres: “Probability on Trees and Networks”, Cambridge University Press, 2017; the book is available on the Web.