15.10.2018:
motivation (random functions, random surfaces)
General theory of Green's functions
Green's functions on graphs, properties.
22.10.2018:
review of Laplacian, Green's functions.
More properties of Green's functions.
DGFF, density, Markov property
5.11.2018:
Review three definitions of DGFF
Continuing Markov property
Continuous Green's function. The existence on simply connected domains.
GFF as a stochastic processes
12.11.2018:
Review Green's function.
Norm (f,g)_G
Def: GFF is a family of Gaussian indexed by f in C^\infty_0(D).
Uniqueness and existence.
Recall distribution (generalized function), H^s.
GFF has a version that is a.s. in H^s whenever s<0 (domain bounded).
In particular, there is a version of GFF which is a.s. a distribution (for any domain).
19.11.2018:
Some remarks about GFF (Fractional Gaussian Fields, log kernel, unbounded domains, construction,...)
Markov's property.
26.11.2018:
Some remarks about Markov's property.
Other remarks.
Circle average.
3.12.2018:
Disk average, Markov's property on circle average.
Thick points. Maximum of GFF.
10.12.2018:
Liouville measure when gamma<\sqrt{2}.
17.12.2018:
Liouville measure (cont.)
Girsanov trick (thick points)
Markov's property of measures
conformal invariance
equivalence of random surfaces
21.1.2018:
28.1.2018: