Organization meeting MVL14 Sept. 3,
12.3013.00 We discuss possible time slots for the course. And I give a very short overview of some of the suggested contents. I will also inform you about the literature and the examination in more detail. 

Some more of the historical background to random walks and discrete potential theory. RW in one dimension, discrete harmonic functions, the maximum principle, the uniquness principle, 
Friday Sept. 7, 1012 MVL15 
Martingales, 2D random walks, the continuous heat equation, Monte Carlo solutions. Electrical networks, see http://www.ece.msstate.edu/~hagler/ece3153/software/software.htmhttp://fy.chalmers.se/%7Epetk/PDF/labbpm.pdf for a Swedish introduction. 
Monday Sept. 10, 1012 MVL15 
Markov Chains,
random walks on more general networks, ergodic and regular Markov
chains. Deadline 1 för uppgifterna: 1.1.21.1.11 (all these are related). 
Friday Sept. 14, 1012 MVL15 Grattis Ida! 
More
general networks. A probabilistic interpretation of voltages and
currents. Effective resistance and escape probability. Energy
minimization  Thompson's principle. 
Måndag 17/9, 1012, MVL15 
Rayleigh's
monotoniciy law and its probabilistic interpretation. 
Måndag 24/9, 1012, MVL15 
Deadline 2 for: 1.2.5, 1.2.7, 1.3.1,
1.3.2,
1.3.5, 1.3.8, 1.3.11, 1.3.12. Laboration! You will work with real (and artificial) circuits with some problems related to the book under the supervision of docent Magnus Karlsteen, Physical Electronics and Photonics at Göteborg University. 
Fredag
28/9, 9.0012.30 (please observe the time) Elektroniklabbet, F7105A i forskarhuset på fysik. 
Polya's
recurrence problem on infinite lattices. Polya's
Theorem. Electrical formulation. 1D. 
Måndag 1/10 
Completion
of the proof of Polya's Thm, for 2D and 3D. A classical proof of Polya's Theorem. 
Fredag 5/10 
Random
walks on more general infinite networks. The kfuzz. 
Måndag 8/10 
More on
the kfuzz. (End of part I) 
Fredag 12/10 
Superharmonic
functions, Green kernel, Harnack inequality Deadline 3: 2.1.2, 2.1.3, 2.1.5, 2.1.6, 2.3.3, 2.3.4, 2.3.6, plus these two final more open problems:

Fredag 19/10 
Isoperimetric
inequalities 
Måndag 22/10 
TBA,
(possible buffer time) 
Fredag 26/10 
Oral examination Friday Nov. 2nd 