Analysis of local growth models.
Lecture 1. Shapes in deterministic and random rules.
Transparencies
in Postscript and
in PDF.
We will introduce basic shape theory for random
monotone local rules,
and will discuss proofs for the existence of such shapes
as well as their characterization through the Wulff construction.
Lecture 2. Toom's methods and applications.
Transparencies
in Postscript and
in PDF.
This talk will discuss properties of growth models
when the updates are nearly deterministic. Sometimes
such random dynamics retain their deterministic
shapes. We will characterize such cases in two
dimensions.
Lecture 3. An exactly solvable growth model.
Transparencies
in Postscript and
in PDF.
Two discrete growth models with an update probability
p will be discussed. One is exactly solvable in the
limit as p goes to 0, the other for every p. The exact
solution allows one to compute the shape explicitly and
to determine the fluctutations around it.
Lecture 4. Critical growth in random environment.
Transparencies
in Postscript and
in PDF.
Bootstrap percolation is a well known model
for rare nucleation. We will review its properties,
focusing on its behavior in an environment of
inert obstacles.
References
in Postscript and
in PDF.