|Organization meeting MVL14 Sept. 3,
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, 10-12
2D random walks, the continuous heat equation, Monte Carlo solutions.
Electrical networks, see
for a Swedish introduction.
|Monday Sept. 10, 10-12
random walks on more general networks, ergodic- and regular Markov
Dead-line 1 för uppgifterna: 1.1.2-1.1.11 (all these are related).
|Friday Sept. 14, 10-12
general networks. A probabilistic interpretation of voltages and
currents. Effective resistance and escape probability. Energy
minimization - Thompson's principle.
||Måndag 17/9, 10-12, MVL15
monotoniciy law and its probabilistic interpretation.
||Måndag 24/9, 10-12, MVL15
|Dead-line 2 for: 1.2.5, 1.2.7, 1.3.1,
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.
28/9, 9.00-12.30 (please observe the time)
Elektroniklabbet, F7105A i forskarhuset på fysik.
recurrence problem on infinite lattices. Polya's
Theorem. Electrical formulation. 1D.
of the proof of Polya's Thm, for 2D and 3D.
A classical proof of Polya's Theorem.
walks on more general infinite networks. The k-fuzz.
the k-fuzz. (End of part I)
functions, Green kernel, Harnack inequality
Dead-line 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:
(possible buffer time)
Oral examination Friday Nov. 2nd